Data description

Important parameters are if the hyoid is fixed or mobile (fixed.hyoid), the condition (or, equivalently, the numeric LEN; see Table below) describing where the hyoid is placed on the vertical dimension, the vowel (i, a, ae, schwa, and u), replication, and the generation when the best elite performance was reached.

Correspondence between ‘condition’ and ‘LEN’.
condition LEN
larynx_1 -9.45
larynx_3 -8.85
larynx_5 -8.25
larynx_7 -7.65
larynx_9 -7.05
larynx_11 -6.45

Each sound is characterized by the first five formants F1F5 as well as by the following 16 articulatory parameters:

## For  [ə]  mobile & fixed intersection is: -8.42  at  0.43 
## For  [ɑ]  mobile & fixed intersection is: -8.4  at  0.43 
## For  [æ]  mobile & fixed intersection is: -8.58  at  0.43 
## For  [i]  mobile & fixed intersection is: -8.3  at  0.43 
## For  [u]  mobile & fixed intersection is: -8.11  at  0.44
Quadratic regression of VTratio on LEN separately for fixed and mobile hyoid by vowel with 95% confidence intervals.

Quadratic regression of VTratio on LEN separately for fixed and mobile hyoid by vowel with 95% confidence intervals.

Regression VTratio on LEN:

## 
## Call:
## lm(formula = VTRatio_elite ~ LEN + I(LEN^2) + vowel + fixed.hyoid, 
##     data = results)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.022870 -0.007136 -0.000362  0.006875  0.025924 
## 
## Coefficients:
##                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      8.533e-01  8.066e-03 105.789  < 2e-16 ***
## LEN              6.682e-02  2.053e-03  32.552  < 2e-16 ***
## I(LEN^2)         2.034e-03  1.289e-04  15.778  < 2e-16 ***
## vowela          -3.288e-05  3.660e-04  -0.090 0.928423    
## vowelae          1.231e-03  3.660e-04   3.363 0.000775 ***
## voweli          -7.909e-04  3.660e-04  -2.161 0.030754 *  
## vowelu          -1.758e-03  3.660e-04  -4.802 1.61e-06 ***
## fixed.hyoidTRUE -7.032e-03  2.315e-04 -30.378  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.008966 on 5992 degrees of freedom
## Multiple R-squared:  0.9403, Adjusted R-squared:  0.9402 
## F-statistic: 1.349e+04 on 7 and 5992 DF,  p-value: < 2.2e-16
Independent t-tests comparinf the VTRatio between the fixed and mobile hyoid for each LEN value (with Bonferroni adjusted p-values).
LEN mean(fixed) mean(mobile) mean(fixed-mobile) t df p Bonferroni-adjusted p
-9.45 0.4071957 0.3908559 0.0163398 -48.63139 499 1.8e-191 1.08e-190
-8.85 0.4211313 0.4162803 0.0048510 -27.99228 499 2.34e-104 1.4e-103
-8.25 0.4360373 0.4390294 -0.0029920 11.98859 499 2.81e-29 1.69e-28
-7.65 0.4520163 0.4592161 -0.0071998 26.87162 499 5e-99 3e-98
-7.05 0.4691827 0.4908364 -0.0216537 72.96072 499 2.28e-268 1.37e-267
-6.45 0.4876670 0.5192070 -0.0315400 151.73500 499 0 0

For each sound, there’s a target (acoustic and articulatory) the same across conditions and replications, and the actual best (or elite) realization in a given condition and replication, from which we also computed the squared error between the target the elite values for each of the F1F5.

The five predefined target vowels.
vowel F1 F2 F3 F4 F5 HX HY JA LP LD TCX TCY TTX TTY TBX TBY SVTv SVTh VTRatio
a 6.59 8.34 15.11 15.91 18.03 0.13 -4.75 -6.73 0.22 2.48 -0.77 -2.53 2.17 -2.16 1.01 -1.28 9.17 7.32 0.44
ae 6.69 12.02 14.69 16.32 18.19 0.34 -3.55 -7.00 0.46 2.54 1.06 -2.06 3.82 -1.75 2.83 -0.83 7.97 7.32 0.48
i 2.29 14.05 15.63 16.52 17.88 1.00 -4.68 -0.98 -0.55 0.28 2.20 -0.71 4.42 -1.17 3.77 0.27 9.10 7.32 0.45
schwa 5.13 9.50 14.55 16.08 18.04 0.99 -4.14 -1.93 0.24 1.66 0.24 -1.33 2.61 -1.70 2.00 -0.48 8.56 7.32 0.46
u 2.72 5.07 15.14 15.79 16.96 1.00 -5.70 -4.57 1.00 0.14 -0.50 -1.32 1.87 -0.41 1.40 0.46 10.14 7.32 0.42
ae 6.68 12.01 14.72 16.33 18.20 0.34 -3.55 -7.00 0.46 2.54 1.06 -2.06 3.82 -1.75 2.83 -0.83 8.00 7.32 0.48

The standard VTL2 and observed LEN and VTLRatio values

The “standard” LEN value for VTL2 is -7.95; we used this value to predict the corresponding VTLRatio in the quadratic regression of VTLRatio ~ LEN + I(LEN^2) + vowel separately for fixed and mobile hyoid per vowel, and we obtained the following point estimates and 95% prediction intervals:

Predicted point estimates (‘fit’) and 95% prediction intervals (‘lwr’–‘upr’) of VTLRatio corresponding to the standard VTL2 LEN value per vowel separately for fixed and mobile hyoid cases.
hyoid LEN vowel fit lwr upr
fixed -7.95 schwa 0.444 0.444 0.444
fixed -7.95 a 0.444 0.444 0.444
fixed -7.95 ae 0.444 0.444 0.444
fixed -7.95 i 0.444 0.444 0.444
fixed -7.95 u 0.444 0.444 0.444
mobile -7.95 schwa 0.450 0.450 0.451
mobile -7.95 a 0.450 0.450 0.451
mobile -7.95 ae 0.453 0.452 0.453
mobile -7.95 i 0.449 0.448 0.449
mobile -7.95 u 0.447 0.446 0.448

Plotting vowels and vowel distinctness in the formant space space

Vowel plots

Fixed hyoid

Mobile hyoid

Stats

F1

##                            Df Sum Sq Mean Sq   F value   Pr(>F)    
## fixed.hyoid                 1      0       0 1.298e+01 0.000318 ***
## VTRatio_elite               1     44      44 2.708e+03  < 2e-16 ***
## I(VTRatio_elite^2)          1      1       1 3.833e+01 6.37e-10 ***
## vowel                       4  17798    4450 2.742e+05  < 2e-16 ***
## replication                 1      0       0 3.000e-03 0.955017    
## fixed.hyoid:vowel           4      1       0 2.135e+01  < 2e-16 ***
## VTRatio_elite:vowel         4     15       4 2.318e+02  < 2e-16 ***
## I(VTRatio_elite^2):vowel    4     22       5 3.383e+02  < 2e-16 ***
## Residuals                5979     97       0                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f1.lm)
## 
## $vowel
##                diff        lwr        upr p adj
## a-schwa   1.2426248  1.2284353  1.2568143     0
## ae-schwa  1.4291830  1.4149935  1.4433725     0
## i-schwa  -2.7672761 -2.7814655 -2.7530866     0
## u-schwa  -2.1399505 -2.1541400 -2.1257610     0
## ae-a      0.1865582  0.1723687  0.2007477     0
## i-a      -4.0099009 -4.0240904 -3.9957114     0
## u-a      -3.3825753 -3.3967648 -3.3683858     0
## i-ae     -4.1964590 -4.2106485 -4.1822695     0
## u-ae     -3.5691335 -3.5833230 -3.5549440     0
## u-i       0.6273256  0.6131361  0.6415151     0
## 
## Call:
## lm(formula = F1_elite ~ fixed.hyoid + VTRatio_elite + I(VTRatio_elite^2) + 
##     vowel + (fixed.hyoid:vowel) + (VTRatio_elite:vowel) + (I(VTRatio_elite^2):vowel) + 
##     replication, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.74278 -0.05434  0.00134  0.04709  1.16453 
## 
## Coefficients:
##                              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                 3.623e+00  5.406e-01   6.702 2.25e-11 ***
## fixed.hyoidTRUE            -1.017e-02  8.101e-03  -1.255  0.20959    
## VTRatio_elite               6.740e+00  2.408e+00   2.799  0.00514 ** 
## I(VTRatio_elite^2)         -7.524e+00  2.659e+00  -2.829  0.00468 ** 
## vowela                     -5.901e+00  7.847e-01  -7.520 6.27e-14 ***
## vowelae                    -1.568e+01  8.463e-01 -18.528  < 2e-16 ***
## voweli                      7.442e+00  7.546e-01   9.863  < 2e-16 ***
## vowelu                      3.981e+00  7.653e-01   5.202 2.04e-07 ***
## replication                -1.329e-05  5.697e-05  -0.233  0.81551    
## fixed.hyoidTRUE:vowela     -8.778e-02  1.141e-02  -7.690 1.70e-14 ***
## fixed.hyoidTRUE:vowelae    -2.331e-02  1.136e-02  -2.053  0.04015 *  
## fixed.hyoidTRUE:voweli      1.770e-02  1.130e-02   1.566  0.11747    
## fixed.hyoidTRUE:vowelu      7.760e-02  1.134e-02   6.846 8.38e-12 ***
## VTRatio_elite:vowela        3.213e+01  3.492e+00   9.201  < 2e-16 ***
## VTRatio_elite:vowelae       7.249e+01  3.750e+00  19.330  < 2e-16 ***
## VTRatio_elite:voweli       -4.670e+01  3.358e+00 -13.906  < 2e-16 ***
## VTRatio_elite:vowelu       -3.026e+01  3.410e+00  -8.875  < 2e-16 ***
## I(VTRatio_elite^2):vowela  -3.567e+01  3.854e+00  -9.255  < 2e-16 ***
## I(VTRatio_elite^2):vowelae -7.605e+01  4.123e+00 -18.446  < 2e-16 ***
## I(VTRatio_elite^2):voweli   5.297e+01  3.708e+00  14.285  < 2e-16 ***
## I(VTRatio_elite^2):vowelu   3.660e+01  3.769e+00   9.713  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1274 on 5979 degrees of freedom
## Multiple R-squared:  0.9946, Adjusted R-squared:  0.9946 
## F-statistic: 5.51e+04 on 20 and 5979 DF,  p-value: < 2.2e-16

F2

##                            Df Sum Sq Mean Sq   F value Pr(>F)    
## fixed.hyoid                 1      0       0 1.033e+00  0.310    
## VTRatio_elite               1    139     139 5.577e+03 <2e-16 ***
## I(VTRatio_elite^2)          1     38      38 1.513e+03 <2e-16 ***
## vowel                       4  51558   12889 5.154e+05 <2e-16 ***
## replication                 1      0       0 4.390e-01  0.508    
## fixed.hyoid:vowel           4      3       1 2.971e+01 <2e-16 ***
## VTRatio_elite:vowel         4    129      32 1.289e+03 <2e-16 ***
## I(VTRatio_elite^2):vowel    4     57      14 5.653e+02 <2e-16 ***
## Residuals                5979    150       0                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f2.lm)
## 
## $vowel
##               diff       lwr       upr p adj
## a-schwa  -1.060586 -1.078202 -1.042970     0
## ae-schwa  2.394547  2.376932  2.412163     0
## i-schwa   4.153959  4.136343  4.171575     0
## u-schwa  -4.368861 -4.386477 -4.351245     0
## ae-a      3.455134  3.437518  3.472750     0
## i-a       5.214545  5.196929  5.232161     0
## u-a      -3.308274 -3.325890 -3.290658     0
## i-ae      1.759411  1.741796  1.777027     0
## u-ae     -6.763408 -6.781024 -6.745792     0
## u-i      -8.522820 -8.540435 -8.505204     0
## 
## Call:
## lm(formula = F2_elite ~ fixed.hyoid + VTRatio_elite + I(VTRatio_elite^2) + 
##     vowel + (fixed.hyoid:vowel) + (VTRatio_elite:vowel) + (I(VTRatio_elite^2):vowel) + 
##     replication, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.84769 -0.05513 -0.00338  0.05541  1.84018 
## 
## Coefficients:
##                              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                 9.788e+00  6.711e-01  14.585  < 2e-16 ***
## fixed.hyoidTRUE             1.099e-02  1.006e-02   1.093 0.274444    
## VTRatio_elite              -1.166e+00  2.989e+00  -0.390 0.696500    
## I(VTRatio_elite^2)          1.157e+00  3.301e+00   0.350 0.726075    
## vowela                      4.576e-01  9.741e-01   0.470 0.638587    
## vowelae                    -1.361e+01  1.051e+00 -12.955  < 2e-16 ***
## voweli                     -3.221e+01  9.368e-01 -34.389  < 2e-16 ***
## vowelu                      2.687e+00  9.501e-01   2.828 0.004697 ** 
## replication                 4.095e-05  7.073e-05   0.579 0.562631    
## fixed.hyoidTRUE:vowela      4.738e-02  1.417e-02   3.344 0.000831 ***
## fixed.hyoidTRUE:vowelae    -3.053e-02  1.410e-02  -2.165 0.030408 *  
## fixed.hyoidTRUE:voweli     -1.832e-01  1.403e-02 -13.051  < 2e-16 ***
## fixed.hyoidTRUE:vowelu      1.680e-02  1.407e-02   1.194 0.232504    
## VTRatio_elite:vowela       -6.942e+00  4.335e+00  -1.601 0.109329    
## VTRatio_elite:vowelae       6.803e+01  4.655e+00  14.613  < 2e-16 ***
## VTRatio_elite:voweli        1.513e+02  4.169e+00  36.290  < 2e-16 ***
## VTRatio_elite:vowelu       -3.370e+01  4.234e+00  -7.960 2.05e-15 ***
## I(VTRatio_elite^2):vowela   7.776e+00  4.784e+00   1.625 0.104143    
## I(VTRatio_elite^2):vowelae -7.156e+01  5.118e+00 -13.980  < 2e-16 ***
## I(VTRatio_elite^2):voweli  -1.551e+02  4.603e+00 -33.689  < 2e-16 ***
## I(VTRatio_elite^2):vowelu   3.975e+01  4.679e+00   8.495  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1581 on 5979 degrees of freedom
## Multiple R-squared:  0.9971, Adjusted R-squared:  0.9971 
## F-statistic: 1.038e+05 on 20 and 5979 DF,  p-value: < 2.2e-16

F3

##                            Df Sum Sq Mean Sq  F value Pr(>F)    
## fixed.hyoid                 1    0.1     0.1    1.611  0.204    
## VTRatio_elite               1  393.1   393.1 4483.146 <2e-16 ***
## I(VTRatio_elite^2)          1  199.6   199.6 2276.929 <2e-16 ***
## vowel                       4  724.7   181.2 2066.126 <2e-16 ***
## replication                 1    0.0     0.0    0.201  0.654    
## fixed.hyoid:vowel           4    9.6     2.4   27.287 <2e-16 ***
## VTRatio_elite:vowel         4   36.9     9.2  105.233 <2e-16 ***
## I(VTRatio_elite^2):vowel    4   24.2     6.0   68.902 <2e-16 ***
## Residuals                5979  524.3     0.1                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f3.lm)
## 
## $vowel
##                  diff         lwr         upr     p adj
## a-schwa   0.376782894  0.34379731  0.40976847 0.0000000
## ae-schwa  0.104717518  0.07173194  0.13770310 0.0000000
## i-schwa   0.999448600  0.96646302  1.03243418 0.0000000
## u-schwa   0.386720547  0.35373497  0.41970613 0.0000000
## ae-a     -0.272065376 -0.30505096 -0.23907980 0.0000000
## i-a       0.622665706  0.58968013  0.65565129 0.0000000
## u-a       0.009937653 -0.02304793  0.04292323 0.9239168
## i-ae      0.894731082  0.86174550  0.92771666 0.0000000
## u-ae      0.282003029  0.24901745  0.31498861 0.0000000
## u-i      -0.612728053 -0.64571363 -0.57974247 0.0000000
## 
## Call:
## lm(formula = F3_elite ~ fixed.hyoid + VTRatio_elite + I(VTRatio_elite^2) + 
##     vowel + (fixed.hyoid:vowel) + (VTRatio_elite:vowel) + (I(VTRatio_elite^2):vowel) + 
##     replication, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.84205 -0.11986 -0.00481  0.12003  2.30041 
## 
## Coefficients:
##                              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                -1.261e+01  1.257e+00 -10.038  < 2e-16 ***
## fixed.hyoidTRUE            -5.689e-02  1.883e-02  -3.021  0.00253 ** 
## VTRatio_elite               1.149e+02  5.598e+00  20.518  < 2e-16 ***
## I(VTRatio_elite^2)         -1.208e+02  6.182e+00 -19.546  < 2e-16 ***
## vowela                     -2.045e+01  1.824e+00 -11.213  < 2e-16 ***
## vowelae                    -9.628e+00  1.967e+00  -4.894 1.01e-06 ***
## voweli                      9.130e+00  1.754e+00   5.205 2.01e-07 ***
## vowelu                      2.089e+00  1.779e+00   1.174  0.24039    
## replication                -6.586e-05  1.324e-04  -0.497  0.61899    
## fixed.hyoidTRUE:vowela     -5.840e-02  2.653e-02  -2.201  0.02777 *  
## fixed.hyoidTRUE:vowelae    -1.191e-02  2.640e-02  -0.451  0.65182    
## fixed.hyoidTRUE:voweli     -6.018e-02  2.628e-02  -2.290  0.02205 *  
## fixed.hyoidTRUE:vowelu     -1.373e-01  2.635e-02  -5.210 1.95e-07 ***
## VTRatio_elite:vowela        8.893e+01  8.117e+00  10.956  < 2e-16 ***
## VTRatio_elite:vowelae       4.157e+01  8.717e+00   4.768 1.90e-06 ***
## VTRatio_elite:voweli       -3.514e+01  7.807e+00  -4.501 6.89e-06 ***
## VTRatio_elite:vowelu       -1.198e+01  7.927e+00  -1.512  0.13068    
## I(VTRatio_elite^2):vowela  -9.397e+01  8.958e+00 -10.490  < 2e-16 ***
## I(VTRatio_elite^2):vowelae -4.398e+01  9.584e+00  -4.589 4.53e-06 ***
## I(VTRatio_elite^2):voweli   3.783e+01  8.619e+00   4.389 1.16e-05 ***
## I(VTRatio_elite^2):vowelu   1.849e+01  8.761e+00   2.110  0.03488 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2961 on 5979 degrees of freedom
## Multiple R-squared:  0.7259, Adjusted R-squared:  0.725 
## F-statistic: 791.6 on 20 and 5979 DF,  p-value: < 2.2e-16

F4

##                            Df Sum Sq Mean Sq  F value Pr(>F)    
## fixed.hyoid                 1    0.1    0.08    0.934  0.334    
## VTRatio_elite               1  173.7  173.70 2130.005 <2e-16 ***
## I(VTRatio_elite^2)          1   11.3   11.35  139.177 <2e-16 ***
## vowel                       4  316.8   79.21  971.285 <2e-16 ***
## replication                 1    0.0    0.01    0.090  0.765    
## fixed.hyoid:vowel           4    8.4    2.09   25.602 <2e-16 ***
## VTRatio_elite:vowel         4   40.3   10.08  123.624 <2e-16 ***
## I(VTRatio_elite^2):vowel    4   31.7    7.92   97.065 <2e-16 ***
## Residuals                5979  487.6    0.08                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f4.lm)
## 
## $vowel
##                 diff         lwr         upr     p adj
## a-schwa  -0.13605756 -0.16786839 -0.10424674 0.0000000
## ae-schwa  0.04414434  0.01233352  0.07595517 0.0014505
## i-schwa   0.50587032  0.47405949  0.53768114 0.0000000
## u-schwa  -0.09170850 -0.12351933 -0.05989768 0.0000000
## ae-a      0.18020191  0.14839108  0.21201273 0.0000000
## i-a       0.64192788  0.61011706  0.67373870 0.0000000
## u-a       0.04434906  0.01253824  0.07615988 0.0013537
## i-ae      0.46172597  0.42991515  0.49353679 0.0000000
## u-ae     -0.13585285 -0.16766367 -0.10404202 0.0000000
## u-i      -0.59757882 -0.62938964 -0.56576800 0.0000000
## 
## Call:
## lm(formula = F4_elite ~ fixed.hyoid + VTRatio_elite + I(VTRatio_elite^2) + 
##     vowel + (fixed.hyoid:vowel) + (VTRatio_elite:vowel) + (I(VTRatio_elite^2):vowel) + 
##     replication, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.09405 -0.15945 -0.03335  0.11293  1.90945 
## 
## Coefficients:
##                              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                 3.773e+00  1.212e+00   3.113 0.001860 ** 
## fixed.hyoidTRUE            -6.028e-02  1.816e-02  -3.319 0.000909 ***
## VTRatio_elite               5.332e+01  5.398e+00   9.877  < 2e-16 ***
## I(VTRatio_elite^2)         -5.713e+01  5.962e+00  -9.583  < 2e-16 ***
## vowela                     -1.241e+01  1.759e+00  -7.053 1.95e-12 ***
## vowelae                    -6.808e+00  1.897e+00  -3.589 0.000335 ***
## voweli                      1.247e+01  1.692e+00   7.370 1.94e-13 ***
## vowelu                      1.886e+01  1.716e+00  10.991  < 2e-16 ***
## replication                -4.508e-05  1.277e-04  -0.353 0.724129    
## fixed.hyoidTRUE:vowela      1.022e-01  2.559e-02   3.995 6.55e-05 ***
## fixed.hyoidTRUE:vowelae     9.559e-02  2.546e-02   3.755 0.000175 ***
## fixed.hyoidTRUE:voweli      8.787e-02  2.534e-02   3.467 0.000530 ***
## fixed.hyoidTRUE:vowelu      1.949e-02  2.541e-02   0.767 0.443108    
## VTRatio_elite:vowela        4.838e+01  7.828e+00   6.181 6.80e-10 ***
## VTRatio_elite:vowelae       2.448e+01  8.407e+00   2.911 0.003611 ** 
## VTRatio_elite:voweli       -5.521e+01  7.529e+00  -7.334 2.54e-13 ***
## VTRatio_elite:vowelu       -8.714e+01  7.645e+00 -11.399  < 2e-16 ***
## I(VTRatio_elite^2):vowela  -4.684e+01  8.639e+00  -5.422 6.11e-08 ***
## I(VTRatio_elite^2):vowelae -2.067e+01  9.243e+00  -2.236 0.025360 *  
## I(VTRatio_elite^2):voweli   6.299e+01  8.312e+00   7.578 4.05e-14 ***
## I(VTRatio_elite^2):vowelu   9.936e+01  8.449e+00  11.760  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2856 on 5979 degrees of freedom
## Multiple R-squared:  0.5443, Adjusted R-squared:  0.5427 
## F-statistic:   357 on 20 and 5979 DF,  p-value: < 2.2e-16

F5

##                            Df Sum Sq Mean Sq F value   Pr(>F)    
## fixed.hyoid                 1   11.7   11.65  219.24  < 2e-16 ***
## VTRatio_elite               1   85.2   85.19 1602.76  < 2e-16 ***
## I(VTRatio_elite^2)          1   99.2   99.17 1865.72  < 2e-16 ***
## vowel                       4  242.4   60.60 1140.18  < 2e-16 ***
## replication                 1    0.2    0.22    4.12   0.0424 *  
## fixed.hyoid:vowel           4    2.4    0.60   11.27 4.16e-09 ***
## VTRatio_elite:vowel         4   53.0   13.24  249.18  < 2e-16 ***
## I(VTRatio_elite^2):vowel    4   97.7   24.43  459.57  < 2e-16 ***
## Residuals                5979  317.8    0.05                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f5.lm)
## 
## $vowel
##                 diff          lwr         upr     p adj
## a-schwa   0.02919600  0.003514457  0.05487754 0.0165407
## ae-schwa  0.10199767  0.076316126  0.12767921 0.0000000
## i-schwa  -0.01270247 -0.038384009  0.01297908 0.6600243
## u-schwa  -0.46280251 -0.488484057 -0.43712097 0.0000000
## ae-a      0.07280167  0.047120126  0.09848321 0.0000000
## i-a      -0.04189847 -0.067580009 -0.01621692 0.0000849
## u-a      -0.49199851 -0.517680056 -0.46631697 0.0000000
## i-ae     -0.11470013 -0.140381677 -0.08901859 0.0000000
## u-ae     -0.56480018 -0.590481725 -0.53911864 0.0000000
## u-i      -0.45010005 -0.475781590 -0.42441851 0.0000000
## 
## Call:
## lm(formula = F5_elite ~ fixed.hyoid + VTRatio_elite + I(VTRatio_elite^2) + 
##     vowel + (fixed.hyoid:vowel) + (VTRatio_elite:vowel) + (I(VTRatio_elite^2):vowel) + 
##     replication, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.55762 -0.11064  0.01865  0.09171  1.33404 
## 
## Coefficients:
##                              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                 2.570e+01  9.784e-01  26.268  < 2e-16 ***
## fixed.hyoidTRUE            -2.141e-02  1.466e-02  -1.460  0.14431    
## VTRatio_elite              -3.465e+01  4.358e+00  -7.951 2.19e-15 ***
## I(VTRatio_elite^2)          3.899e+01  4.813e+00   8.100 6.61e-16 ***
## vowela                      2.816e+00  1.420e+00   1.983  0.04745 *  
## vowelae                    -4.653e-01  1.532e+00  -0.304  0.76130    
## voweli                      3.366e+00  1.366e+00   2.465  0.01374 *  
## vowelu                      4.542e+01  1.385e+00  32.787  < 2e-16 ***
## replication                -2.167e-04  1.031e-04  -2.102  0.03561 *  
## fixed.hyoidTRUE:vowela      2.927e-02  2.066e-02   1.417  0.15663    
## fixed.hyoidTRUE:vowelae    -5.834e-03  2.055e-02  -0.284  0.77654    
## fixed.hyoidTRUE:voweli      5.098e-02  2.046e-02   2.492  0.01273 *  
## fixed.hyoidTRUE:vowelu      2.093e-01  2.052e-02  10.203  < 2e-16 ***
## VTRatio_elite:vowela       -1.438e+01  6.320e+00  -2.275  0.02296 *  
## VTRatio_elite:vowelae       1.070e+00  6.787e+00   0.158  0.87470    
## VTRatio_elite:voweli       -1.697e+01  6.078e+00  -2.792  0.00526 ** 
## VTRatio_elite:vowelu       -2.122e+02  6.172e+00 -34.389  < 2e-16 ***
## I(VTRatio_elite^2):vowela   1.798e+01  6.974e+00   2.578  0.00995 ** 
## I(VTRatio_elite^2):vowelae  4.087e-01  7.462e+00   0.055  0.95633    
## I(VTRatio_elite^2):voweli   2.074e+01  6.711e+00   3.090  0.00201 ** 
## I(VTRatio_elite^2):vowelu   2.430e+02  6.821e+00  35.628  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2305 on 5979 degrees of freedom
## Multiple R-squared:  0.6506, Adjusted R-squared:  0.6494 
## F-statistic: 556.6 on 20 and 5979 DF,  p-value: < 2.2e-16

Summarized

Summary of F1–F5 regressions with betas (for non-factor DVs and ‘.’ for factors), p-values, and adjusted R2. Interactions are denoted by ‘:’.
DVs, interactions & R2 F1 F2 F3 F4 F5
fixed.hyoid -0.01 (0.21) 0.011 (0.27) -0.057 (0.0025**) -0.06 (0.00091***) -0.021 (0.14)
VTRatio_elite 6.7 (0.0051**) -1.2 (0.7) 1.1e+02 (1.8e-90***) 53 (7.9e-23***) -35 (2.2e-15***)
VTRatio_elite^2 -7.5 (0.0047**) 1.2 (0.73) -1.2e+02 (1.6e-82***) -57 (1.3e-21***) 39 (6.6e-16***)
vowel . (0***) . (0***) . (0***) . (0***) . (0***)
replication -1.3e-05 (0.82) 4.1e-05 (0.56) -6.6e-05 (0.62) -4.5e-05 (0.72) -0.00022 (0.036*)
fixed.hyoid:vowel . (1.7e-17***) . (1.7e-24***) . (1.8e-22***) . (4.6e-21***) . (4.2e-09***)
VTRatio_elite:vowel . (2.5e-185***) . (0***) . (9.2e-87***) . (1.6e-101***) . (2.8e-198***)
VTRatio_elite^2:vowel . (6.8e-263***) . (0***) . (4.1e-57***) . (3.8e-80***) . (0***)
adjusted R2 99.5% 99.7% 72.5% 54.3% 64.9%
Predicted formants for each LEN per vowel pair. (95% prediction intervals are too narrow to show.)

Predicted formants for each LEN per vowel pair. (95% prediction intervals are too narrow to show.)

For mobile hyoid only

F1

##                            Df Sum Sq Mean Sq   F value Pr(>F)    
## VTRatio_elite               1     47    47.0 2.880e+03 <2e-16 ***
## I(VTRatio_elite^2)          1      1     1.1 6.936e+01 <2e-16 ***
## vowel                       4   8870  2217.5 1.357e+05 <2e-16 ***
## replication                 1      0     0.0 6.270e-01  0.428    
## VTRatio_elite:vowel         4      9     2.1 1.305e+02 <2e-16 ***
## I(VTRatio_elite^2):vowel    4     14     3.5 2.163e+02 <2e-16 ***
## Residuals                2984     49     0.0                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f1.lm)
## 
## $vowel
##                diff        lwr        upr p adj
## a-schwa   1.2653481  1.2452059  1.2854903     0
## ae-schwa  1.4167198  1.3965776  1.4368620     0
## i-schwa  -2.7417014 -2.7618436 -2.7215591     0
## u-schwa  -2.1471948 -2.1673371 -2.1270526     0
## ae-a      0.1513717  0.1312295  0.1715139     0
## i-a      -4.0070494 -4.0271916 -3.9869072     0
## u-a      -3.4125429 -3.4326851 -3.3924007     0
## i-ae     -4.1584211 -4.1785633 -4.1382789     0
## u-ae     -3.5639146 -3.5840568 -3.5437724     0
## u-i       0.5945065  0.5743643  0.6146487     0
## 
## Call:
## lm(formula = F1_elite ~ VTRatio_elite + I(VTRatio_elite^2) + 
##     vowel + (VTRatio_elite:vowel) + (I(VTRatio_elite^2):vowel) + 
##     replication, data = d[!d$fixed.hyoid, ])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.75362 -0.04972  0.00095  0.04754  1.17084 
## 
## Coefficients:
##                              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                 3.393e+00  5.888e-01   5.762 9.16e-09 ***
## VTRatio_elite               7.760e+00  2.611e+00   2.972  0.00298 ** 
## I(VTRatio_elite^2)         -8.656e+00  2.871e+00  -3.015  0.00259 ** 
## vowela                     -5.034e+00  8.613e-01  -5.845 5.61e-09 ***
## vowelae                    -1.393e+01  9.750e-01 -14.285  < 2e-16 ***
## voweli                      7.030e+00  8.214e-01   8.559  < 2e-16 ***
## vowelu                      2.556e+00  8.322e-01   3.071  0.00215 ** 
## replication                 4.498e-05  8.085e-05   0.556  0.57797    
## VTRatio_elite:vowela        2.749e+01  3.814e+00   7.208 7.17e-13 ***
## VTRatio_elite:vowelae       6.470e+01  4.290e+00  15.084  < 2e-16 ***
## VTRatio_elite:voweli       -4.491e+01  3.638e+00 -12.346  < 2e-16 ***
## VTRatio_elite:vowelu       -2.414e+01  3.692e+00  -6.538 7.32e-11 ***
## I(VTRatio_elite^2):vowela  -2.970e+01  4.190e+00  -7.090 1.67e-12 ***
## I(VTRatio_elite^2):vowelae -6.748e+01  4.683e+00 -14.409  < 2e-16 ***
## I(VTRatio_elite^2):voweli   5.105e+01  3.998e+00  12.767  < 2e-16 ***
## I(VTRatio_elite^2):vowelu   3.008e+01  4.063e+00   7.404 1.71e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1278 on 2984 degrees of freedom
## Multiple R-squared:  0.9946, Adjusted R-squared:  0.9945 
## F-statistic: 3.648e+04 on 15 and 2984 DF,  p-value: < 2.2e-16

F2

##                            Df Sum Sq Mean Sq   F value Pr(>F)    
## VTRatio_elite               1    104     104 4.510e+03 <2e-16 ***
## I(VTRatio_elite^2)          1     34      34 1.477e+03 <2e-16 ***
## vowel                       4  25849    6462 2.800e+05 <2e-16 ***
## replication                 1      0       0 1.610e-01  0.688    
## VTRatio_elite:vowel         4     59      15 6.338e+02 <2e-16 ***
## I(VTRatio_elite^2):vowel    4     29       7 3.093e+02 <2e-16 ***
## Residuals                2984     69       0                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f2.lm)
## 
## $vowel
##               diff       lwr       upr p adj
## a-schwa  -1.082595 -1.106534 -1.058655     0
## ae-schwa  2.376443  2.352503  2.400382     0
## i-schwa   4.193568  4.169629  4.217508     0
## u-schwa  -4.346817 -4.370756 -4.322877     0
## ae-a      3.459038  3.435098  3.482977     0
## i-a       5.276163  5.252224  5.300102     0
## u-a      -3.264222 -3.288161 -3.240283     0
## i-ae      1.817125  1.793186  1.841065     0
## u-ae     -6.723259 -6.747199 -6.699320     0
## u-i      -8.540385 -8.564324 -8.516446     0
## 
## Call:
## lm(formula = F2_elite ~ VTRatio_elite + I(VTRatio_elite^2) + 
##     vowel + (VTRatio_elite:vowel) + (I(VTRatio_elite^2):vowel) + 
##     replication, data = d[!d$fixed.hyoid, ])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.77908 -0.05154 -0.00058  0.05810  1.80438 
## 
## Coefficients:
##                              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                 9.312e+00  6.998e-01  13.306  < 2e-16 ***
## VTRatio_elite               8.630e-01  3.103e+00   0.278    0.781    
## I(VTRatio_elite^2)         -9.769e-01  3.413e+00  -0.286    0.775    
## vowela                     -1.742e-02  1.024e+00  -0.017    0.986    
## vowelae                    -1.314e+01  1.159e+00 -11.342  < 2e-16 ***
## voweli                     -2.283e+01  9.762e-01 -23.383  < 2e-16 ***
## vowelu                      1.490e+00  9.891e-01   1.507    0.132    
## replication                 2.498e-05  9.609e-05   0.260    0.795    
## VTRatio_elite:vowela       -4.398e+00  4.533e+00  -0.970    0.332    
## VTRatio_elite:vowelae       6.572e+01  5.098e+00  12.891  < 2e-16 ***
## VTRatio_elite:voweli        1.113e+02  4.324e+00  25.750  < 2e-16 ***
## VTRatio_elite:vowelu       -2.903e+01  4.388e+00  -6.617 4.34e-11 ***
## I(VTRatio_elite^2):vowela   4.503e+00  4.979e+00   0.904    0.366    
## I(VTRatio_elite^2):vowelae -6.877e+01  5.566e+00 -12.354  < 2e-16 ***
## I(VTRatio_elite^2):voweli  -1.130e+02  4.752e+00 -23.777  < 2e-16 ***
## I(VTRatio_elite^2):vowelu   3.533e+01  4.829e+00   7.315 3.28e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1519 on 2984 degrees of freedom
## Multiple R-squared:  0.9974, Adjusted R-squared:  0.9974 
## F-statistic: 7.532e+04 on 15 and 2984 DF,  p-value: < 2.2e-16

F3

##                            Df Sum Sq Mean Sq  F value Pr(>F)    
## VTRatio_elite               1  175.1  175.08 1739.560 <2e-16 ***
## I(VTRatio_elite^2)          1   94.4   94.37  937.598 <2e-16 ***
## vowel                       4  407.0  101.75 1010.957 <2e-16 ***
## replication                 1    0.0    0.00    0.034  0.853    
## VTRatio_elite:vowel         4   19.6    4.91   48.744 <2e-16 ***
## I(VTRatio_elite^2):vowel    4   30.4    7.59   75.403 <2e-16 ***
## Residuals                2984  300.3    0.10                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f3.lm)
## 
## $vowel
##                diff         lwr        upr p adj
## a-schwa   0.3696720  0.31967824  0.4196659 0e+00
## ae-schwa  0.1057591  0.05576528  0.1557529 1e-07
## i-schwa   1.0513291  1.00133531  1.1013229 0e+00
## u-schwa   0.4783480  0.42835418  0.5283418 0e+00
## ae-a     -0.2639130 -0.31390676 -0.2139192 0e+00
## i-a       0.6816571  0.63166326  0.7316509 0e+00
## u-a       0.1086759  0.05868213  0.1586697 0e+00
## i-ae      0.9455700  0.89557622  0.9955638 0e+00
## u-ae      0.3725889  0.32259509  0.4225827 0e+00
## u-i      -0.5729811 -0.62297493 -0.5229873 0e+00
## 
## Call:
## lm(formula = F3_elite ~ VTRatio_elite + I(VTRatio_elite^2) + 
##     vowel + (VTRatio_elite:vowel) + (I(VTRatio_elite^2):vowel) + 
##     replication, data = d[!d$fixed.hyoid, ])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.80440 -0.11711  0.00607  0.12020  1.84341 
## 
## Coefficients:
##                              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                -1.118e+01  1.462e+00  -7.647 2.75e-14 ***
## VTRatio_elite               1.082e+02  6.480e+00  16.690  < 2e-16 ***
## I(VTRatio_elite^2)         -1.131e+02  7.127e+00 -15.877  < 2e-16 ***
## vowela                     -1.553e+01  2.138e+00  -7.263 4.81e-13 ***
## vowelae                    -9.870e+00  2.420e+00  -4.079 4.65e-05 ***
## voweli                      1.448e+01  2.039e+00   7.103 1.52e-12 ***
## vowelu                      1.654e+01  2.066e+00   8.008 1.65e-15 ***
## replication                 2.542e-05  2.007e-04   0.127 0.899197    
## VTRatio_elite:vowela        6.731e+01  9.466e+00   7.111 1.44e-12 ***
## VTRatio_elite:vowelae       4.232e+01  1.065e+01   3.975 7.22e-05 ***
## VTRatio_elite:voweli       -5.712e+01  9.030e+00  -6.326 2.90e-10 ***
## VTRatio_elite:vowelu       -7.257e+01  9.163e+00  -7.921 3.31e-15 ***
## I(VTRatio_elite^2):vowela  -7.047e+01  1.040e+01  -6.776 1.48e-11 ***
## I(VTRatio_elite^2):vowelae -4.445e+01  1.162e+01  -3.824 0.000134 ***
## I(VTRatio_elite^2):voweli   6.006e+01  9.924e+00   6.052 1.61e-09 ***
## I(VTRatio_elite^2):vowelu   8.118e+01  1.008e+01   8.049 1.19e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3173 on 2984 degrees of freedom
## Multiple R-squared:  0.7075, Adjusted R-squared:  0.706 
## F-statistic: 481.2 on 15 and 2984 DF,  p-value: < 2.2e-16

F4

##                            Df Sum Sq Mean Sq F value  Pr(>F)    
## VTRatio_elite               1  57.27   57.27 771.255 < 2e-16 ***
## I(VTRatio_elite^2)          1   0.80    0.80  10.711 0.00108 ** 
## vowel                       4 165.33   41.33 556.607 < 2e-16 ***
## replication                 1   0.04    0.04   0.497 0.48102    
## VTRatio_elite:vowel         4  17.70    4.43  59.600 < 2e-16 ***
## I(VTRatio_elite^2):vowel    4  25.24    6.31  84.966 < 2e-16 ***
## Residuals                2984 221.58    0.07                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f4.lm)
## 
## $vowel
##                 diff         lwr          upr     p adj
## a-schwa  -0.18780768 -0.23074936 -0.144865994 0.0000000
## ae-schwa  0.02453996 -0.01840172  0.067481645 0.5234953
## i-schwa   0.50724987  0.46430818  0.550191552 0.0000000
## u-schwa  -0.03593817 -0.07887985  0.007003517 0.1501842
## ae-a      0.21234764  0.16940596  0.255289323 0.0000000
## i-a       0.69505755  0.65211586  0.737999229 0.0000000
## u-a       0.15186951  0.10892783  0.194811195 0.0000000
## i-ae      0.48270991  0.43976822  0.525651590 0.0000000
## u-ae     -0.06047813 -0.10341981 -0.017536444 0.0011666
## u-i      -0.54318803 -0.58612972 -0.500246351 0.0000000
## 
## Call:
## lm(formula = F4_elite ~ VTRatio_elite + I(VTRatio_elite^2) + 
##     vowel + (VTRatio_elite:vowel) + (I(VTRatio_elite^2):vowel) + 
##     replication, data = d[!d$fixed.hyoid, ])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.23313 -0.13599 -0.03896  0.08959  1.71957 
## 
## Coefficients:
##                              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                 7.799e+00  1.255e+00   6.213 5.93e-10 ***
## VTRatio_elite               3.587e+01  5.566e+00   6.445 1.35e-10 ***
## I(VTRatio_elite^2)         -3.847e+01  6.121e+00  -6.284 3.78e-10 ***
## vowela                     -8.176e+00  1.836e+00  -4.453 8.79e-06 ***
## vowelae                    -6.177e+00  2.079e+00  -2.972 0.002982 ** 
## voweli                      8.371e+00  1.751e+00   4.781 1.83e-06 ***
## vowelu                      2.265e+01  1.774e+00  12.766  < 2e-16 ***
## replication                 1.107e-04  1.724e-04   0.642 0.520720    
## VTRatio_elite:vowela        3.175e+01  8.131e+00   3.905 9.64e-05 ***
## VTRatio_elite:vowelae       2.188e+01  9.145e+00   2.393 0.016789 *  
## VTRatio_elite:voweli       -3.701e+01  7.756e+00  -4.773 1.91e-06 ***
## VTRatio_elite:vowelu       -1.022e+02  7.870e+00 -12.987  < 2e-16 ***
## I(VTRatio_elite^2):vowela  -3.089e+01  8.932e+00  -3.458 0.000552 ***
## I(VTRatio_elite^2):vowelae -1.800e+01  9.985e+00  -1.803 0.071455 .  
## I(VTRatio_elite^2):voweli   4.297e+01  8.524e+00   5.041 4.92e-07 ***
## I(VTRatio_elite^2):vowelu   1.140e+02  8.662e+00  13.159  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2725 on 2984 degrees of freedom
## Multiple R-squared:  0.5459, Adjusted R-squared:  0.5436 
## F-statistic: 239.1 on 15 and 2984 DF,  p-value: < 2.2e-16

F5

##                            Df Sum Sq Mean Sq  F value Pr(>F)    
## VTRatio_elite               1  79.60   79.60 1773.443 <2e-16 ***
## I(VTRatio_elite^2)          1  67.90   67.90 1512.727 <2e-16 ***
## vowel                       4 101.02   25.25  562.645 <2e-16 ***
## replication                 1   0.04    0.04    0.796  0.372    
## VTRatio_elite:vowel         4  23.45    5.86  130.627 <2e-16 ***
## I(VTRatio_elite^2):vowel    4  89.24   22.31  497.033 <2e-16 ***
## Residuals                2984 133.94    0.04                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f5.lm)
## 
## $vowel
##                 diff           lwr         upr     p adj
## a-schwa   0.03397099  0.0005851859  0.06735679 0.0437960
## ae-schwa  0.11405633  0.0806705288  0.14744213 0.0000000
## i-schwa  -0.01635768 -0.0497434872  0.01702812 0.6678401
## u-schwa  -0.41145974 -0.4448455438 -0.37807394 0.0000000
## ae-a      0.08008534  0.0466995405  0.11347115 0.0000000
## i-a      -0.05032867 -0.0837144754 -0.01694287 0.0003834
## u-a      -0.44543073 -0.4788165321 -0.41204493 0.0000000
## i-ae     -0.13041402 -0.1637998183 -0.09702821 0.0000000
## u-ae     -0.52551607 -0.5589018750 -0.49213027 0.0000000
## u-i      -0.39510206 -0.4284878590 -0.36171625 0.0000000
## 
## Call:
## lm(formula = F5_elite ~ VTRatio_elite + I(VTRatio_elite^2) + 
##     vowel + (VTRatio_elite:vowel) + (I(VTRatio_elite^2):vowel) + 
##     replication, data = d[!d$fixed.hyoid, ])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.33741 -0.11438  0.01260  0.08843  1.28819 
## 
## Coefficients:
##                              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                 2.228e+01  9.760e-01  22.828  < 2e-16 ***
## VTRatio_elite              -2.018e+01  4.327e+00  -4.662 3.27e-06 ***
## I(VTRatio_elite^2)          2.383e+01  4.759e+00   5.007 5.84e-07 ***
## vowela                      3.514e+00  1.428e+00   2.461  0.01390 *  
## vowelae                    -1.847e+00  1.616e+00  -1.143  0.25308    
## voweli                      5.513e+00  1.361e+00   4.050 5.26e-05 ***
## vowelu                      4.828e+01  1.379e+00  35.000  < 2e-16 ***
## replication                -1.335e-04  1.340e-04  -0.997  0.31907    
## VTRatio_elite:vowela       -1.742e+01  6.322e+00  -2.756  0.00588 ** 
## VTRatio_elite:vowelae       6.815e+00  7.110e+00   0.958  0.33791    
## VTRatio_elite:voweli       -2.557e+01  6.030e+00  -4.240 2.30e-05 ***
## VTRatio_elite:vowelu       -2.225e+02  6.119e+00 -36.368  < 2e-16 ***
## I(VTRatio_elite^2):vowela   2.127e+01  6.944e+00   3.063  0.00221 ** 
## I(VTRatio_elite^2):vowelae -5.519e+00  7.763e+00  -0.711  0.47714    
## I(VTRatio_elite^2):voweli   2.916e+01  6.627e+00   4.401 1.12e-05 ***
## I(VTRatio_elite^2):vowelu   2.516e+02  6.735e+00  37.366  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2119 on 2984 degrees of freedom
## Multiple R-squared:  0.7295, Adjusted R-squared:  0.7282 
## F-statistic: 536.5 on 15 and 2984 DF,  p-value: < 2.2e-16

Summarized

Summary of F1–F5 regressions with betas (for non-factor DVs and ‘.’ for factors), p-values, and adjusted R2. Interactions are denoted by ‘:’.
DVs, interactions & R2 F1 F2 F3 F4 F5
VTRatio_elite 7.8 (0.003**) 0.86 (0.78) 1.1e+02 (7.4e-60***) 36 (1.3e-10***) -20 (3.3e-06***)
VTRatio_elite^2 -8.7 (0.0026**) -0.98 (0.77) -1.1e+02 (1.5e-54***) -38 (3.8e-10***) 24 (5.8e-07***)
vowel . (0***) . (0***) . (0***) . (0***) . (0***)
replication 4.5e-05 (0.58) 2.5e-05 (0.79) 2.5e-05 (0.9) 0.00011 (0.52) -0.00013 (0.32)
VTRatio_elite:vowel . (7.6e-103***) . (0***) . (9e-40***) . (1.7e-48***) . (6.2e-103***)
VTRatio_elite^2:vowel . (3.4e-163***) . (8.2e-223***) . (5.6e-61***) . (2e-68***) . (0***)
adjusted R2 99.5% 99.7% 70.6% 54.4% 72.8%

Difficulty in learning vowels

A proxy for “learning difficulty” is represented (in principle) by the time-to-plateau (i.e., generation, with lower meaning “easier to learn”):

##                  Df   Sum Sq Mean Sq F value   Pr(>F)    
## vowel             4  3047077  761769  85.377  < 2e-16 ***
## LEN               1   434699  434699  48.720 3.62e-12 ***
## I(LEN^2)          1  1284719 1284719 143.988  < 2e-16 ***
## replication       1    14237   14237   1.596    0.207    
## vowel:LEN         4  1263758  315940  35.410  < 2e-16 ***
## vowel:I(LEN^2)    4   894256  223564  25.056  < 2e-16 ***
## Residuals      2984 26624496    8922                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## LEN
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## I(LEN^2)
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## replication
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## vowel, LEN
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## vowel, I(LEN^2)
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = time.to.plateau)
## 
## $vowel
##              diff        lwr        upr     p adj
## [ɑ]-[ə]  40.10667  25.221461  54.991872 0.0000000
## [æ]-[ə] -26.28500 -41.170206 -11.399794 0.0000149
## [i]-[ə]  -6.63000 -21.515206   8.255206 0.7422552
## [u]-[ə]  60.40667  45.521461  75.291872 0.0000000
## [æ]-[ɑ] -66.39167 -81.276872 -51.506461 0.0000000
## [i]-[ɑ] -46.73667 -61.621872 -31.851461 0.0000000
## [u]-[ɑ]  20.30000   5.414794  35.185206 0.0018782
## [i]-[æ]  19.65500   4.769794  34.540206 0.0029385
## [u]-[æ]  86.69167  71.806461 101.576872 0.0000000
## [u]-[i]  67.03667  52.151461  81.921872 0.0000000
## 
## Call:
## lm(formula = generation ~ vowel + LEN + I(LEN^2) + (vowel:LEN) + 
##     (vowel:I(LEN^2)) + replication, data = d)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -249.52  -62.23   -9.11   52.96  360.17 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)        2.877e+03  2.686e+02  10.711  < 2e-16 ***
## vowel[ɑ]          -7.497e+02  3.799e+02  -1.974  0.04852 *  
## vowel[æ]          -6.091e+01  3.799e+02  -0.160  0.87261    
## vowel[i]          -2.165e+03  3.799e+02  -5.700 1.31e-08 ***
## vowel[u]          -2.897e+03  3.799e+02  -7.626 3.24e-14 ***
## LEN                7.029e+02  6.838e+01  10.279  < 2e-16 ***
## I(LEN^2)           4.473e+01  4.294e+00  10.417  < 2e-16 ***
## replication       -7.547e-02  5.974e-02  -1.263  0.20662    
## vowel[ɑ]:LEN      -2.373e+02  9.671e+01  -2.454  0.01420 *  
## vowel[æ]:LEN      -4.716e+01  9.671e+01  -0.488  0.62583    
## vowel[i]:LEN      -5.437e+02  9.671e+01  -5.622 2.06e-08 ***
## vowel[u]:LEN      -7.956e+02  9.671e+01  -8.227 2.84e-16 ***
## vowel[ɑ]:I(LEN^2) -1.707e+01  6.073e+00  -2.810  0.00498 ** 
## vowel[æ]:I(LEN^2) -5.296e+00  6.073e+00  -0.872  0.38324    
## vowel[i]:I(LEN^2) -3.367e+01  6.073e+00  -5.545 3.20e-08 ***
## vowel[u]:I(LEN^2) -5.242e+01  6.073e+00  -8.631  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 94.46 on 2984 degrees of freedom
## Multiple R-squared:  0.2067, Adjusted R-squared:  0.2027 
## F-statistic: 51.85 on 15 and 2984 DF,  p-value: < 2.2e-16
Summary of generations to plateau regressions with betas (for non-factor DVs and ‘.’ for factors), p-values, and adjusted R2. Interactions are denoted by ‘:’.
DVs, interactions & R2 Gens.to.plateau
vowel . (9.5e-69***)
LEN 7e+02 (2.2e-24***)
LEN^2 45 (5.5e-25***)
replication -0.075 (0.21)
vowel:LEN . (6.1e-29***)
vowel:LEN^2 . (1.9e-20***)
adjusted R2 20.3%

Formants predicted by condition, vowel and generation

Mobile hyoid

F1 and error

##                  Df Sum Sq Mean Sq   F value   Pr(>F)    
## LEN               1     11    11.3 6.946e+02  < 2e-16 ***
## I(LEN^2)          1      0     0.5 3.064e+01 3.37e-08 ***
## vowel             4   8907  2226.7 1.370e+05  < 2e-16 ***
## replication       1      0     0.0 6.570e-01    0.418    
## generation        1      2     1.7 1.057e+02  < 2e-16 ***
## LEN:vowel         4      9     2.3 1.412e+02  < 2e-16 ***
## I(LEN^2):vowel    4     11     2.8 1.749e+02  < 2e-16 ***
## Residuals      2983     48     0.0                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f1.lm)
## 
## $vowel
##                diff        lwr        upr p adj
## a-schwa   1.2662947  1.2462044  1.2863849     0
## ae-schwa  1.4269103  1.4068201  1.4470006     0
## i-schwa  -2.7444628 -2.7645531 -2.7243726     0
## u-schwa  -2.1558078 -2.1758981 -2.1357176     0
## ae-a      0.1606157  0.1405254  0.1807059     0
## i-a      -4.0107575 -4.0308478 -3.9906672     0
## u-a      -3.4221025 -3.4421928 -3.4020122     0
## i-ae     -4.1713732 -4.1914634 -4.1512829     0
## u-ae     -3.5827182 -3.6028084 -3.5626279     0
## u-i       0.5886550  0.5685647  0.6087453     0
## 
## Call:
## lm(formula = F1_elite ~ LEN + I(LEN^2) + vowel + (LEN:vowel) + 
##     (I(LEN^2):vowel) + replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.71892 -0.05245 -0.00138  0.05277  1.15894 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       4.624e+00  3.694e-01  12.517  < 2e-16 ***
## LEN              -1.291e-01  9.391e-02  -1.374    0.169    
## I(LEN^2)         -7.754e-03  5.900e-03  -1.314    0.189    
## vowela           -2.064e+00  5.130e-01  -4.023 5.89e-05 ***
## vowelae          -3.472e+00  5.127e-01  -6.773 1.52e-11 ***
## voweli            3.624e+00  5.155e-01   7.030 2.55e-12 ***
## vowelu            2.111e+00  5.177e-01   4.077 4.67e-05 ***
## replication       4.727e-05  8.066e-05   0.586    0.558    
## generation       -2.397e-04  2.471e-05  -9.703  < 2e-16 ***
## LEN:vowela       -8.812e-01  1.307e-01  -6.745 1.83e-11 ***
## LEN:vowelae      -1.380e+00  1.305e-01 -10.570  < 2e-16 ***
## LEN:voweli        1.571e+00  1.312e-01  11.975  < 2e-16 ***
## LEN:vowelu        9.468e-01  1.320e-01   7.173 9.21e-13 ***
## I(LEN^2):vowela  -5.706e-02  8.207e-03  -6.952 4.41e-12 ***
## I(LEN^2):vowelae -9.455e-02  8.198e-03 -11.534  < 2e-16 ***
## I(LEN^2):voweli   9.528e-02  8.239e-03  11.565  < 2e-16 ***
## I(LEN^2):vowelu   5.098e-02  8.298e-03   6.143 9.18e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1275 on 2983 degrees of freedom
## Multiple R-squared:  0.9946, Adjusted R-squared:  0.9946 
## F-statistic: 3.438e+04 on 16 and 2983 DF,  p-value: < 2.2e-16
##                  Df Sum Sq Mean Sq F value   Pr(>F)    
## LEN               1   0.40   0.405  27.682 1.53e-07 ***
## I(LEN^2)          1   3.34   3.343 228.593  < 2e-16 ***
## vowel             4   5.46   1.364  93.252  < 2e-16 ***
## replication       1   0.05   0.046   3.131   0.0769 .  
## generation        1   2.20   2.205 150.738  < 2e-16 ***
## LEN:vowel         4   7.98   1.996 136.483  < 2e-16 ***
## I(LEN^2):vowel    4   0.80   0.201  13.720 4.34e-11 ***
## Residuals      2983  43.63   0.015                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f1e.lm)
## 
## $vowel
##                  diff          lwr         upr     p adj
## a-schwa   0.054684170  0.035626048  0.07374229 0.0000000
## ae-schwa  0.046145752  0.027087629  0.06520387 0.0000000
## i-schwa   0.022666699  0.003608576  0.04172482 0.0103877
## u-schwa   0.126216379  0.107158257  0.14527450 0.0000000
## ae-a     -0.008538419 -0.027596541  0.01051970 0.7380593
## i-a      -0.032017471 -0.051075594 -0.01295935 0.0000463
## u-a       0.071532209  0.052474087  0.09059033 0.0000000
## i-ae     -0.023479053 -0.042537175 -0.00442093 0.0069959
## u-ae      0.080070628  0.061012505  0.09912875 0.0000000
## u-i       0.103549680  0.084491558  0.12260780 0.0000000
## 
## Call:
## lm(formula = F1.error ~ LEN + I(LEN^2) + vowel + (LEN:vowel) + 
##     (I(LEN^2):vowel) + replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.37891 -0.03064 -0.00755  0.01857  2.44618 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       1.018e+00  3.505e-01   2.906 0.003693 ** 
## LEN               2.513e-01  8.909e-02   2.821 0.004826 ** 
## I(LEN^2)          1.591e-02  5.597e-03   2.842 0.004519 ** 
## vowela            1.852e+00  4.867e-01   3.805 0.000144 ***
## vowelae           2.656e+00  4.863e-01   5.461 5.13e-08 ***
## voweli            1.126e+00  4.890e-01   2.303 0.021366 *  
## vowelu            3.925e+00  4.911e-01   7.993 1.86e-15 ***
## replication       1.139e-04  7.651e-05   1.489 0.136569    
## generation       -2.838e-04  2.344e-05 -12.109  < 2e-16 ***
## LEN:vowela        4.536e-01  1.239e-01   3.660 0.000257 ***
## LEN:vowelae       7.146e-01  1.238e-01   5.771 8.69e-09 ***
## LEN:voweli        2.696e-01  1.245e-01   2.166 0.030393 *  
## LEN:vowelu        8.546e-01  1.252e-01   6.825 1.06e-11 ***
## I(LEN^2):vowela   2.833e-02  7.786e-03   3.639 0.000278 ***
## I(LEN^2):vowelae  4.768e-02  7.777e-03   6.132 9.83e-10 ***
## I(LEN^2):voweli   1.616e-02  7.815e-03   2.067 0.038785 *  
## I(LEN^2):vowelu   4.688e-02  7.872e-03   5.955 2.90e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1209 on 2983 degrees of freedom
## Multiple R-squared:  0.3169, Adjusted R-squared:  0.3133 
## F-statistic:  86.5 on 16 and 2983 DF,  p-value: < 2.2e-16

F2

##                  Df Sum Sq Mean Sq   F value Pr(>F)    
## LEN               1     44      44 2.163e+03 <2e-16 ***
## I(LEN^2)          1      7       7 3.355e+02 <2e-16 ***
## vowel             4  25939    6485 3.171e+05 <2e-16 ***
## replication       1      0       0 2.020e-01  0.653    
## generation        1      2       2 1.191e+02 <2e-16 ***
## LEN:vowel         4     61      15 7.416e+02 <2e-16 ***
## I(LEN^2):vowel    4     29       7 3.485e+02 <2e-16 ***
## Residuals      2983     61       0                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f2.lm)
## 
## $vowel
##               diff       lwr       upr p adj
## a-schwa  -1.076651 -1.099186 -1.054116     0
## ae-schwa  2.404134  2.381599  2.426669     0
## i-schwa   4.196537  4.174002  4.219072     0
## u-schwa  -4.353799 -4.376334 -4.331264     0
## ae-a      3.480784  3.458249  3.503319     0
## i-a       5.273188  5.250653  5.295723     0
## u-a      -3.277148 -3.299683 -3.254613     0
## i-ae      1.792404  1.769869  1.814939     0
## u-ae     -6.757933 -6.780468 -6.735397     0
## u-i      -8.550336 -8.572871 -8.527801     0
## 
## Call:
## lm(formula = F2_elite ~ LEN + I(LEN^2) + vowel + (LEN:vowel) + 
##     (I(LEN^2):vowel) + replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.76663 -0.05060 -0.00369  0.05095  1.85656 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       9.718e+00  4.144e-01  23.450  < 2e-16 ***
## LEN               5.292e-02  1.053e-01   0.502    0.615    
## I(LEN^2)          3.491e-03  6.618e-03   0.528    0.598    
## vowela           -5.281e-01  5.755e-01  -0.918    0.359    
## vowelae          -3.133e+00  5.751e-01  -5.447 5.52e-08 ***
## voweli           -7.769e+00  5.782e-01 -13.437  < 2e-16 ***
## vowelu            7.929e-01  5.807e-01   1.365    0.172    
## replication       3.067e-05  9.047e-05   0.339    0.735    
## generation       -1.318e-04  2.771e-05  -4.755 2.08e-06 ***
## LEN:vowela        1.474e-01  1.466e-01   1.006    0.315    
## LEN:vowelae      -1.536e+00  1.464e-01 -10.493  < 2e-16 ***
## LEN:voweli       -3.452e+00  1.472e-01 -23.452  < 2e-16 ***
## LEN:vowelu        1.184e+00  1.481e-01   7.996 1.83e-15 ***
## I(LEN^2):vowela   9.786e-03  9.206e-03   1.063    0.288    
## I(LEN^2):vowelae -1.040e-01  9.195e-03 -11.308  < 2e-16 ***
## I(LEN^2):voweli  -2.409e-01  9.241e-03 -26.064  < 2e-16 ***
## I(LEN^2):vowelu   6.650e-02  9.308e-03   7.144 1.13e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.143 on 2983 degrees of freedom
## Multiple R-squared:  0.9977, Adjusted R-squared:  0.9977 
## F-statistic: 7.971e+04 on 16 and 2983 DF,  p-value: < 2.2e-16
##                  Df Sum Sq Mean Sq F value  Pr(>F)    
## LEN               1  19.24  19.236 570.924 < 2e-16 ***
## I(LEN^2)          1  22.38  22.380 664.225 < 2e-16 ***
## vowel             4  50.08  12.520 371.589 < 2e-16 ***
## replication       1   0.00   0.003   0.101 0.75092    
## generation        1   0.34   0.335   9.946 0.00163 ** 
## LEN:vowel         4  93.96  23.490 697.189 < 2e-16 ***
## I(LEN^2):vowel    4  40.50  10.126 300.543 < 2e-16 ***
## Residuals      2983 100.51   0.034                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f2e.lm)
## 
## $vowel
##                  diff          lwr         upr     p adj
## a-schwa   0.009513431 -0.019412150  0.03843901 0.8978329
## ae-schwa  0.033145297  0.004219716  0.06207088 0.0153061
## i-schwa   0.346381443  0.317455863  0.37530702 0.0000000
## u-schwa   0.084291067  0.055365486  0.11321665 0.0000000
## ae-a      0.023631866 -0.005293715  0.05255745 0.1689003
## i-a       0.336868013  0.307942432  0.36579359 0.0000000
## u-a       0.074777636  0.045852055  0.10370322 0.0000000
## i-ae      0.313236146  0.284310566  0.34216173 0.0000000
## u-ae      0.051145770  0.022220189  0.08007135 0.0000144
## u-i      -0.262090376 -0.291015957 -0.23316480 0.0000000
## 
## Call:
## lm(formula = F2.error ~ LEN + I(LEN^2) + vowel + (LEN:vowel) + 
##     (I(LEN^2):vowel) + replication + generation, data = d)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.5844 -0.0373 -0.0055  0.0241  4.6120 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       1.008e+00  5.319e-01   1.895 0.058149 .  
## LEN               2.476e-01  1.352e-01   1.831 0.067161 .  
## I(LEN^2)          1.577e-02  8.495e-03   1.856 0.063506 .  
## vowela           -1.668e-01  7.386e-01  -0.226 0.821363    
## vowelae           2.359e+00  7.382e-01   3.196 0.001409 ** 
## voweli            1.837e+01  7.422e-01  24.759  < 2e-16 ***
## vowelu            4.199e+00  7.453e-01   5.633 1.93e-08 ***
## replication      -5.927e-05  1.161e-04  -0.510 0.609829    
## generation       -2.970e-04  3.557e-05  -8.349  < 2e-16 ***
## LEN:vowela       -5.560e-02  1.881e-01  -0.296 0.767572    
## LEN:vowelae       6.324e-01  1.879e-01   3.365 0.000775 ***
## LEN:voweli        5.037e+00  1.889e-01  26.662  < 2e-16 ***
## LEN:vowelu        9.655e-01  1.900e-01   5.080 4.00e-07 ***
## I(LEN^2):vowela  -3.950e-03  1.182e-02  -0.334 0.738172    
## I(LEN^2):vowelae  4.193e-02  1.180e-02   3.552 0.000388 ***
## I(LEN^2):voweli   3.426e-01  1.186e-02  28.882  < 2e-16 ***
## I(LEN^2):vowelu   5.571e-02  1.195e-02   4.663 3.26e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1836 on 2983 degrees of freedom
## Multiple R-squared:  0.6926, Adjusted R-squared:  0.691 
## F-statistic: 420.2 on 16 and 2983 DF,  p-value: < 2.2e-16

F3

##                  Df Sum Sq Mean Sq  F value Pr(>F)    
## LEN               1  213.5  213.47 2299.192 <2e-16 ***
## I(LEN^2)          1   94.8   94.78 1020.771 <2e-16 ***
## vowel             4  397.4   99.36 1070.144 <2e-16 ***
## replication       1    0.0    0.00    0.044  0.834    
## generation        1    0.2    0.23    2.434  0.119    
## LEN:vowel         4   19.2    4.79   51.644 <2e-16 ***
## I(LEN^2):vowel    4   24.7    6.18   66.539 <2e-16 ***
## Residuals      2983  277.0    0.09                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f3.lm)
## 
## $vowel
##                diff         lwr        upr   p adj
## a-schwa   0.3796662  0.33164887  0.4276835 0.0e+00
## ae-schwa  0.1479860  0.09996871  0.1960033 0.0e+00
## i-schwa   1.0587442  1.01072687  1.1067615 0.0e+00
## u-schwa   0.4722282  0.42421087  0.5202455 0.0e+00
## ae-a     -0.2316802 -0.27969746 -0.1836629 0.0e+00
## i-a       0.6790780  0.63106071  0.7270953 0.0e+00
## u-a       0.0925620  0.04454471  0.1405793 1.5e-06
## i-ae      0.9107582  0.86274087  0.9587755 0.0e+00
## u-ae      0.3242422  0.27622487  0.3722595 0.0e+00
## u-i      -0.5865160 -0.63453329 -0.5384987 0.0e+00
## 
## Call:
## lm(formula = F3_elite ~ LEN + I(LEN^2) + vowel + (LEN:vowel) + 
##     (I(LEN^2):vowel) + replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.78577 -0.10898 -0.00001  0.10983  1.82683 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       2.141e+00  8.830e-01   2.424   0.0154 *  
## LEN              -3.373e+00  2.245e-01 -15.028  < 2e-16 ***
## I(LEN^2)         -2.273e-01  1.410e-02 -16.118  < 2e-16 ***
## vowela           -6.354e+00  1.226e+00  -5.182 2.34e-07 ***
## vowelae          -5.794e-01  1.225e+00  -0.473   0.6364    
## voweli            6.758e+00  1.232e+00   5.486 4.47e-08 ***
## vowelu            1.151e+01  1.237e+00   9.303  < 2e-16 ***
## replication       4.658e-05  1.928e-04   0.242   0.8091    
## generation        8.062e-05  5.905e-05   1.365   0.1723    
## LEN:vowela       -1.857e+00  3.123e-01  -5.946 3.07e-09 ***
## LEN:vowelae      -1.945e-01  3.120e-01  -0.623   0.5331    
## LEN:voweli        1.566e+00  3.136e-01   4.994 6.27e-07 ***
## LEN:vowelu        2.765e+00  3.155e-01   8.763  < 2e-16 ***
## I(LEN^2):vowela  -1.250e-01  1.962e-02  -6.371 2.16e-10 ***
## I(LEN^2):vowelae -1.271e-02  1.959e-02  -0.649   0.5166    
## I(LEN^2):voweli   1.051e-01  1.969e-02   5.336 1.02e-07 ***
## I(LEN^2):vowelu   1.702e-01  1.983e-02   8.581  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3047 on 2983 degrees of freedom
## Multiple R-squared:  0.7303, Adjusted R-squared:  0.7288 
## F-statistic: 504.7 on 16 and 2983 DF,  p-value: < 2.2e-16
##                  Df Sum Sq Mean Sq  F value Pr(>F)    
## LEN               1  336.8   336.8 2401.950 <2e-16 ***
## I(LEN^2)          1  205.5   205.5 1465.412 <2e-16 ***
## vowel             4   72.2    18.0  128.683 <2e-16 ***
## replication       1    0.0     0.0    0.063  0.801    
## generation        1   18.3    18.3  130.308 <2e-16 ***
## LEN:vowel         4   91.4    22.8  162.889 <2e-16 ***
## I(LEN^2):vowel    4   61.0    15.3  108.804 <2e-16 ***
## Residuals      2983  418.3     0.1                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f3e.lm)
## 
## $vowel
##                 diff         lwr         upr     p adj
## a-schwa   0.24590068  0.18689104  0.30491032 0.0000000
## ae-schwa  0.01228932 -0.04672032  0.07129896 0.9796108
## i-schwa  -0.02238000 -0.08138964  0.03662964 0.8390675
## u-schwa   0.36119025  0.30218060  0.42019989 0.0000000
## ae-a     -0.23361136 -0.29262100 -0.17460172 0.0000000
## i-a      -0.26828068 -0.32729032 -0.20927104 0.0000000
## u-a       0.11528957  0.05627992  0.17429921 0.0000010
## i-ae     -0.03466932 -0.09367896  0.02434032 0.4951256
## u-ae      0.34890093  0.28989128  0.40791057 0.0000000
## u-i       0.38357025  0.32456060  0.44257989 0.0000000
## 
## Call:
## lm(formula = F3.error ~ LEN + I(LEN^2) + vowel + (LEN:vowel) + 
##     (I(LEN^2):vowel) + replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.85790 -0.11849 -0.00991  0.10380  2.67903 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       1.373e+01  1.085e+00  12.651  < 2e-16 ***
## LEN               3.681e+00  2.758e-01  13.343  < 2e-16 ***
## I(LEN^2)          2.454e-01  1.733e-02  14.160  < 2e-16 ***
## vowela            1.678e+01  1.507e+00  11.133  < 2e-16 ***
## vowelae          -1.956e+00  1.506e+00  -1.299    0.194    
## voweli           -8.459e+00  1.514e+00  -5.587 2.51e-08 ***
## vowelu            8.111e+00  1.520e+00   5.335 1.03e-07 ***
## replication       2.269e-05  2.369e-04   0.096    0.924    
## generation       -4.896e-04  7.257e-05  -6.746 1.82e-11 ***
## LEN:vowela        4.536e+00  3.838e-01  11.821  < 2e-16 ***
## LEN:vowelae      -5.201e-01  3.834e-01  -1.357    0.175    
## LEN:voweli       -2.257e+00  3.854e-01  -5.857 5.22e-09 ***
## LEN:vowelu        2.299e+00  3.877e-01   5.929 3.39e-09 ***
## I(LEN^2):vowela   3.043e-01  2.411e-02  12.624  < 2e-16 ***
## I(LEN^2):vowelae -3.392e-02  2.408e-02  -1.409    0.159    
## I(LEN^2):voweli  -1.480e-01  2.420e-02  -6.118 1.07e-09 ***
## I(LEN^2):vowelu   1.643e-01  2.437e-02   6.740 1.90e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3745 on 2983 degrees of freedom
## Multiple R-squared:  0.6524, Adjusted R-squared:  0.6506 
## F-statistic:   350 on 16 and 2983 DF,  p-value: < 2.2e-16

F4

##                  Df Sum Sq Mean Sq F value   Pr(>F)    
## LEN               1  65.88   65.88 915.085  < 2e-16 ***
## I(LEN^2)          1   0.56    0.56   7.716  0.00551 ** 
## vowel             4 164.02   41.00 569.533  < 2e-16 ***
## replication       1   0.04    0.04   0.539  0.46289    
## generation        1   2.81    2.81  39.088 4.63e-10 ***
## LEN:vowel         4  19.05    4.76  66.166  < 2e-16 ***
## I(LEN^2):vowel    4  20.82    5.21  72.300  < 2e-16 ***
## Residuals      2983 214.76    0.07                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f4.lm)
## 
## $vowel
##                 diff          lwr          upr     p adj
## a-schwa  -0.18706467 -0.229347849 -0.144781484 0.0000000
## ae-schwa  0.03495083 -0.007332349  0.077234016 0.1596788
## i-schwa   0.50373283  0.461449651  0.546016016 0.0000000
## u-schwa  -0.04582850 -0.088111682 -0.003545318 0.0258936
## ae-a      0.22201550  0.179732318  0.264298682 0.0000000
## i-a       0.69079750  0.648514318  0.733080682 0.0000000
## u-a       0.14123617  0.098952984  0.183519349 0.0000000
## i-ae      0.46878200  0.426498818  0.511065182 0.0000000
## u-ae     -0.08077933 -0.123062516 -0.038496151 0.0000020
## u-i      -0.54956133 -0.591844516 -0.507278151 0.0000000
## 
## Call:
## lm(formula = F4_elite ~ LEN + I(LEN^2) + vowel + (LEN:vowel) + 
##     (I(LEN^2):vowel) + replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.31160 -0.13988 -0.02858  0.09520  1.64294 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      12.2559754  0.7775637  15.762  < 2e-16 ***
## LEN              -1.0363722  0.1976581  -5.243 1.69e-07 ***
## I(LEN^2)         -0.0680677  0.0124182  -5.481 4.58e-08 ***
## vowela           -1.8431068  1.0797328  -1.707  0.08793 .  
## vowelae           2.8151681  1.0790335   2.609  0.00913 ** 
## voweli            8.0354463  1.0848880   7.407 1.68e-13 ***
## vowelu           13.8142052  1.0894926  12.679  < 2e-16 ***
## replication       0.0001035  0.0001698   0.610  0.54197    
## generation       -0.0002791  0.0000520  -5.368 8.59e-08 ***
## LEN:vowela       -0.6025396  0.2749866  -2.191  0.02852 *  
## LEN:vowelae       0.4976349  0.2747206   1.811  0.07018 .  
## LEN:voweli        1.8445077  0.2761606   6.679 2.86e-11 ***
## LEN:vowelu        3.4884375  0.2778076  12.557  < 2e-16 ***
## I(LEN^2):vowela  -0.0486044  0.0172740  -2.814  0.00493 ** 
## I(LEN^2):vowelae  0.0181883  0.0172534   1.054  0.29188    
## I(LEN^2):voweli   0.1109727  0.0173398   6.400 1.80e-10 ***
## I(LEN^2):vowelu   0.2161769  0.0174651  12.378  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2683 on 2983 degrees of freedom
## Multiple R-squared:  0.5599, Adjusted R-squared:  0.5575 
## F-statistic: 237.2 on 16 and 2983 DF,  p-value: < 2.2e-16
##                  Df Sum Sq Mean Sq F value Pr(>F)    
## LEN               1   0.11   0.114   1.300  0.254    
## I(LEN^2)          1   6.12   6.125  69.930 <2e-16 ***
## vowel             4  23.65   5.912  67.500 <2e-16 ***
## replication       1   0.00   0.004   0.043  0.835    
## generation        1  13.71  13.707 156.508 <2e-16 ***
## LEN:vowel         4  14.76   3.691  42.146 <2e-16 ***
## I(LEN^2):vowel    4  12.96   3.240  36.996 <2e-16 ***
## Residuals      2983 261.26   0.088                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f4e.lm)
## 
## $vowel
##                 diff         lwr         upr     p adj
## a-schwa   0.07531938  0.02868309 0.121955664 0.0001054
## ae-schwa  0.08824385  0.04160756 0.134880140 0.0000025
## i-schwa   0.05149025  0.00485396 0.098126536 0.0218916
## u-schwa   0.26251898  0.21588269 0.309155268 0.0000000
## ae-a      0.01292448 -0.03371181 0.059560763 0.9428703
## i-a      -0.02382913 -0.07046542 0.022807160 0.6311783
## u-a       0.18719960  0.14056332 0.233835892 0.0000000
## i-ae     -0.03675360 -0.08338989 0.009882684 0.1989404
## u-ae      0.17427513  0.12763884 0.220911417 0.0000000
## u-i       0.21102873  0.16439244 0.257665020 0.0000000
## 
## Call:
## lm(formula = F4.error ~ LEN + I(LEN^2) + vowel + (LEN:vowel) + 
##     (I(LEN^2):vowel) + replication + generation, data = d)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.7485 -0.0849 -0.0326  0.0459  4.3436 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       1.402e+00  8.576e-01   1.635 0.102142    
## LEN               3.421e-01  2.180e-01   1.569 0.116715    
## I(LEN^2)          2.249e-02  1.370e-02   1.642 0.100658    
## vowela           -1.963e+00  1.191e+00  -1.648 0.099435 .  
## vowelae           3.470e+00  1.190e+00   2.916 0.003575 ** 
## voweli            5.162e-01  1.197e+00   0.431 0.666239    
## vowelu            1.197e+01  1.202e+00   9.960  < 2e-16 ***
## replication      -5.014e-06  1.872e-04  -0.027 0.978636    
## generation       -5.833e-04  5.736e-05 -10.170  < 2e-16 ***
## LEN:vowela       -5.247e-01  3.033e-01  -1.730 0.083725 .  
## LEN:vowelae       9.642e-01  3.030e-01   3.182 0.001477 ** 
## LEN:voweli        5.172e-02  3.046e-01   0.170 0.865170    
## LEN:vowelu        2.871e+00  3.064e-01   9.371  < 2e-16 ***
## I(LEN^2):vowela  -3.284e-02  1.905e-02  -1.724 0.084868 .  
## I(LEN^2):vowelae  6.643e-02  1.903e-02   3.491 0.000489 ***
## I(LEN^2):voweli  -8.923e-04  1.912e-02  -0.047 0.962790    
## I(LEN^2):vowelu   1.736e-01  1.926e-02   9.014  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2959 on 2983 degrees of freedom
## Multiple R-squared:  0.2145, Adjusted R-squared:  0.2102 
## F-statistic:  50.9 on 16 and 2983 DF,  p-value: < 2.2e-16

F5

##                  Df Sum Sq Mean Sq  F value Pr(>F)    
## LEN               1  65.93   65.93 1520.677 <2e-16 ***
## I(LEN^2)          1  77.15   77.15 1779.445 <2e-16 ***
## vowel             4 106.48   26.62  613.995 <2e-16 ***
## replication       1   0.03    0.03    0.744  0.389    
## generation        1   6.42    6.42  148.158 <2e-16 ***
## LEN:vowel         4  19.37    4.84  111.700 <2e-16 ***
## I(LEN^2):vowel    4  90.46   22.62  521.652 <2e-16 ***
## Residuals      2983 129.33    0.04                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f5.lm)
## 
## $vowel
##                 diff          lwr          upr     p adj
## a-schwa   0.02494017 -0.007871841  0.057752175 0.2313571
## ae-schwa  0.09895817  0.066146159  0.131770175 0.0000000
## i-schwa  -0.03595900 -0.068771008 -0.003146992 0.0234372
## u-schwa  -0.43585017 -0.468662175 -0.403038159 0.0000000
## ae-a      0.07401800  0.041205992  0.106830008 0.0000000
## i-a      -0.06089917 -0.093711175 -0.028087159 0.0000043
## u-a      -0.46079033 -0.493602341 -0.427978325 0.0000000
## i-ae     -0.13491717 -0.167729175 -0.102105159 0.0000000
## u-ae     -0.53480833 -0.567620341 -0.501996325 0.0000000
## u-i      -0.39989117 -0.432703175 -0.367079159 0.0000000
## 
## Call:
## lm(formula = F5_elite ~ LEN + I(LEN^2) + vowel + (LEN:vowel) + 
##     (I(LEN^2):vowel) + replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.16825 -0.10985  0.00877  0.09293  1.36548 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       2.332e+01  6.034e-01  38.655  < 2e-16 ***
## LEN               1.265e+00  1.534e-01   8.248 2.39e-16 ***
## I(LEN^2)          7.574e-02  9.637e-03   7.859 5.34e-15 ***
## vowela            2.452e+00  8.379e-01   2.927  0.00345 ** 
## vowelae           1.138e-01  8.373e-01   0.136  0.89191    
## voweli            2.532e+00  8.419e-01   3.007  0.00266 ** 
## vowelu            3.242e+01  8.455e-01  38.343  < 2e-16 ***
## replication      -1.388e-04  1.317e-04  -1.054  0.29212    
## generation       -3.344e-04  4.035e-05  -8.286  < 2e-16 ***
## LEN:vowela        5.222e-01  2.134e-01   2.447  0.01446 *  
## LEN:vowelae      -9.328e-02  2.132e-01  -0.438  0.66174    
## LEN:voweli        6.251e-01  2.143e-01   2.917  0.00356 ** 
## LEN:vowelu        8.173e+00  2.156e-01  37.911  < 2e-16 ***
## I(LEN^2):vowela   2.704e-02  1.340e-02   2.017  0.04376 *  
## I(LEN^2):vowelae -1.191e-02  1.339e-02  -0.890  0.37380    
## I(LEN^2):voweli   3.734e-02  1.346e-02   2.775  0.00555 ** 
## I(LEN^2):vowelu   5.002e-01  1.355e-02  36.910  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2082 on 2983 degrees of freedom
## Multiple R-squared:  0.7388, Adjusted R-squared:  0.7374 
## F-statistic: 527.4 on 16 and 2983 DF,  p-value: < 2.2e-16
##                  Df Sum Sq Mean Sq  F value Pr(>F)    
## LEN               1   78.9   78.94  826.584 <2e-16 ***
## I(LEN^2)          1  162.8  162.76 1704.212 <2e-16 ***
## vowel             4  363.9   90.98  952.642 <2e-16 ***
## replication       1    0.1    0.07    0.707  0.401    
## generation        1   14.3   14.30  149.726 <2e-16 ***
## LEN:vowel         4  170.6   42.65  446.635 <2e-16 ***
## I(LEN^2):vowel    4  349.2   87.30  914.151 <2e-16 ***
## Residuals      2983  284.9    0.10                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f5e.lm)
## 
## $vowel
##                 diff          lwr        upr     p adj
## a-schwa  0.017963483 -0.030735666 0.06666263 0.8523528
## ae-schwa 0.023620836 -0.025078313 0.07231998 0.6763185
## i-schwa  0.050998397  0.002299248 0.09969755 0.0347793
## u-schwa  0.892911019  0.844211871 0.94161017 0.0000000
## ae-a     0.005657353 -0.043041796 0.05435650 0.9978132
## i-a      0.033034914 -0.015664234 0.08173406 0.3441483
## u-a      0.874947537  0.826248388 0.92364669 0.0000000
## i-ae     0.027377561 -0.021321587 0.07607671 0.5400289
## u-ae     0.869290184  0.820591035 0.91798933 0.0000000
## u-i      0.841912622  0.793213474 0.89061177 0.0000000
## 
## Call:
## lm(formula = F5.error ~ LEN + I(LEN^2) + vowel + (LEN:vowel) + 
##     (I(LEN^2):vowel) + replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.70174 -0.05366 -0.00684  0.03785  2.68674 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       4.010e+00  8.955e-01   4.477 7.84e-06 ***
## LEN               9.752e-01  2.277e-01   4.284 1.90e-05 ***
## I(LEN^2)          5.998e-02  1.430e-02   4.193 2.83e-05 ***
## vowela            1.577e+00  1.244e+00   1.268    0.205    
## vowelae           1.750e+00  1.243e+00   1.408    0.159    
## voweli            1.992e+00  1.250e+00   1.594    0.111    
## vowelu            6.642e+01  1.255e+00  52.932  < 2e-16 ***
## replication      -1.971e-04  1.955e-04  -1.008    0.313    
## generation       -4.353e-04  5.989e-05  -7.269 4.61e-13 ***
## LEN:vowela        3.451e-01  3.167e-01   1.089    0.276    
## LEN:vowelae       4.184e-01  3.164e-01   1.322    0.186    
## LEN:voweli        4.585e-01  3.181e-01   1.441    0.150    
## LEN:vowelu        1.614e+01  3.200e-01  50.436  < 2e-16 ***
## I(LEN^2):vowela   1.870e-02  1.990e-02   0.940    0.347    
## I(LEN^2):vowelae  2.471e-02  1.987e-02   1.244    0.214    
## I(LEN^2):voweli   2.648e-02  1.997e-02   1.326    0.185    
## I(LEN^2):vowelu   9.773e-01  2.012e-02  48.584  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.309 on 2983 degrees of freedom
## Multiple R-squared:    0.8,  Adjusted R-squared:  0.799 
## F-statistic: 745.9 on 16 and 2983 DF,  p-value: < 2.2e-16

Summarized

Summary of F1–F5 regressions with betas (for non-factor DVs and ‘.’ for factors), p-values, and adjusted R2. Interactions are denoted by ‘:’.
DVs, interactions & R2 F1 F1 error F2 F2 error F3 F3 error F4 F4 error F5 F5 error
LEN -0.13 (0.17) 0.25 (0.0048**) 0.053 (0.62) 0.25 (0.067) -3.4 (2.9e-49***) 3.7 (1.7e-39***) -1 (1.7e-07***) 0.34 (0.12) 1.3 (2.4e-16***) 0.98 (1.9e-05***)
LEN^2 -0.0078 (0.19) 0.016 (0.0045**) 0.0035 (0.6) 0.016 (0.064) -0.23 (4.2e-56***) 0.25 (4.2e-44***) -0.068 (4.6e-08***) 0.022 (0.1) 0.076 (5.3e-15***) 0.06 (2.8e-05***)
vowel . (0***) . (8e-75***) . (0***) . (6.3e-260***) . (0***) . (1.7e-101***) . (0***) . (9.3e-55***) . (0***) . (0***)
replication 4.7e-05 (0.56) 0.00011 (0.14) 3.1e-05 (0.73) -5.9e-05 (0.61) 4.7e-05 (0.81) 2.3e-05 (0.92) 0.0001 (0.54) -5e-06 (0.98) -0.00014 (0.29) -0.0002 (0.31)
generation -0.00024 (6.2e-22***) -0.00028 (5.6e-33***) -0.00013 (2.1e-06***) -0.0003 (1e-16***) 8.1e-05 (0.17) -0.00049 (1.8e-11***) -0.00028 (8.6e-08***) -0.00058 (6.6e-24***) -0.00033 (1.8e-16***) -0.00044 (4.6e-13***)
LEN:vowel . (1.1e-110***) . (3.2e-107***) . (0***) . (0***) . (4.1e-42***) . (2.9e-126***) . (1.1e-53***) . (2e-34***) . (7.6e-89***) . (5.6e-302***)
LEN^2:vowel . (8.8e-135***) . (4.3e-11***) . (2.2e-246***) . (2e-217***) . (5.4e-54***) . (1.2e-86***) . (1.5e-58***) . (3.1e-30***) . (0***) . (0***)
adjusted R2 99.5% 31.3% 99.8% 69.1% 72.9% 65.1% 55.8% 21.0% 73.7% 79.9%
Formants for each vowel per condition for mobile hyoid.

Formants for each vowel per condition for mobile hyoid.

Predicted formants for each vowel per condition for mobile hyoid. (95% prediction intervals are too narrow to show.)

Predicted formants for each vowel per condition for mobile hyoid. (95% prediction intervals are too narrow to show.)

Predicted formants for each vowel per condition for mobile hyoid. (95% prediction intervals are too narrow to show.)

Predicted formants for each vowel per condition for mobile hyoid. (95% prediction intervals are too narrow to show.)

Scaled predicted formants for each vowel per condition for mobile hyoid. (95% prediction intervals are not shown).

Scaled predicted formants for each vowel per condition for mobile hyoid. (95% prediction intervals are not shown).

Predicted acoustic errors for each vowel per condition for mobile hyoid. (95% prediction intervals are too narrow to show.)

Predicted acoustic errors for each vowel per condition for mobile hyoid. (95% prediction intervals are too narrow to show.)

Predicted acoustic errors for each vowel per condition for mobile hyoid. (95% prediction intervals are too narrow to show.)

Predicted acoustic errors for each vowel per condition for mobile hyoid. (95% prediction intervals are too narrow to show.)

Inter-vowel distances

F1–F5

##                                 Df Sum Sq Mean Sq   F value Pr(>F)    
## VTRatio_elite                    1     24    23.7   466.251 <2e-16 ***
## I(VTRatio_elite^2)               1    105   105.4  2074.671 <2e-16 ***
## vowel.pair                       9  24922  2769.1 54523.114 <2e-16 ***
## replication                      1      0     0.1     2.294   0.13    
## VTRatio_elite:vowel.pair         9    166    18.4   362.653 <2e-16 ***
## I(VTRatio_elite^2):vowel.pair    9     29     3.2    63.901 <2e-16 ***
## Residuals                     5969    303     0.1                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = ive15.lm)
## 
## $vowel.pair
##                        diff         lwr        upr p adj
## a-i-a-ae          3.2206040  3.17942457  3.2617834     0
## a-schwa-a-ae     -1.7595631 -1.80074257 -1.7183837     0
## a-u-a-ae          1.3600053  1.31882590  1.4011848     0
## ae-i-a-ae         1.1763889  1.13520949  1.2175684     0
## ae-schwa-a-ae    -0.6914381 -0.73261752 -0.6502586     0
## ae-u-a-ae         4.2238993  4.18271988  4.2650787     0
## i-schwa-a-ae      1.6718153  1.63063591  1.7129948     0
## i-u-a-ae          5.1604378  5.11925838  5.2016172     0
## schwa-u-a-ae      1.4910841  1.44990464  1.5322635     0
## a-schwa-a-i      -4.9801671 -5.02134656 -4.9389877     0
## a-u-a-i          -1.8605987 -1.90177810 -1.8194192     0
## ae-i-a-i         -2.0442151 -2.08539451 -2.0030356     0
## ae-schwa-a-i     -3.9120421 -3.95322151 -3.8708626     0
## ae-u-a-i          1.0032953  0.96211588  1.0444747     0
## i-schwa-a-i      -1.5487887 -1.58996809 -1.5076092     0
## i-u-a-i           1.9398338  1.89865438  1.9810132     0
## schwa-u-a-i      -1.7295199 -1.77069936 -1.6883405     0
## a-u-a-schwa       3.1195685  3.07838903  3.1607479     0
## ae-i-a-schwa      2.9359521  2.89477262  2.9771315     0
## ae-schwa-a-schwa  1.0681250  1.02694562  1.1093045     0
## ae-u-a-schwa      5.9834624  5.94228301  6.0246419     0
## i-schwa-a-schwa   3.4313785  3.39019904  3.4725579     0
## i-u-a-schwa       6.9200009  6.87882151  6.9611804     0
## schwa-u-a-schwa   3.2506472  3.20946777  3.2918266     0
## ae-i-a-u         -0.1836164 -0.22479584 -0.1424370     0
## ae-schwa-a-u     -2.0514434 -2.09262285 -2.0102640     0
## ae-u-a-u          2.8638940  2.82271455  2.9050734     0
## i-schwa-a-u       0.3118100  0.27063058  0.3529894     0
## i-u-a-u           3.8004325  3.75925305  3.8416119     0
## schwa-u-a-u       0.1310787  0.08989931  0.1722582     0
## ae-schwa-ae-i    -1.8678270 -1.90900644 -1.8266476     0
## ae-u-ae-i         3.0475104  3.00633096  3.0886898     0
## i-schwa-ae-i      0.4954264  0.45424699  0.5366059     0
## i-u-ae-i          3.9840489  3.94286946  4.0252283     0
## schwa-u-ae-i      0.3146951  0.27351571  0.3558746     0
## ae-u-ae-schwa     4.9153374  4.87415796  4.9565168     0
## i-schwa-ae-schwa  2.3632534  2.32207399  2.4044329     0
## i-u-ae-schwa      5.8518759  5.81069646  5.8930553     0
## schwa-u-ae-schwa  2.1825222  2.14134272  2.2237016     0
## i-schwa-ae-u     -2.5520840 -2.59326340 -2.5109045     0
## i-u-ae-u          0.9365385  0.89535907  0.9777179     0
## schwa-u-ae-u     -2.7328152 -2.77399468 -2.6916358     0
## i-u-i-schwa       3.4886225  3.44744304  3.5298019     0
## schwa-u-i-schwa  -0.1807313 -0.22191070 -0.1395518     0
## schwa-u-i-u      -3.6693537 -3.71053318 -3.6281743     0
## 
## Call:
## lm(formula = dist_elite_F1F5 ~ VTRatio_elite + I(VTRatio_elite^2) + 
##     vowel.pair + (VTRatio_elite:vowel.pair) + (I(VTRatio_elite^2):vowel.pair) + 
##     replication, data = intervowel.dists[intervowel.dists$fixed.hyoid == 
##     FALSE, ])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.63591 -0.09749  0.01613  0.11363  0.98443 
## 
## Coefficients:
##                                         Estimate Std. Error t value
## (Intercept)                           -9.219e+00  1.108e+00  -8.318
## VTRatio_elite                          5.350e+01  4.902e+00  10.914
## I(VTRatio_elite^2)                    -5.546e+01  5.379e+00 -10.310
## vowel.paira-i                         -1.010e+01  1.567e+00  -6.441
## vowel.paira-schwa                      6.350e+00  1.567e+00   4.051
## vowel.paira-u                          7.572e+00  1.567e+00   4.831
## vowel.pairae-i                        -5.079e+00  1.567e+00  -3.240
## vowel.pairae-schwa                    -1.879e+00  1.567e+00  -1.199
## vowel.pairae-u                        -5.082e+00  1.567e+00  -3.242
## vowel.pairi-schwa                     -8.337e+00  1.567e+00  -5.319
## vowel.pairi-u                         -1.626e+01  1.567e+00 -10.371
## vowel.pairschwa-u                      1.064e+01  1.567e+00   6.786
## replication                           -1.527e-04  1.008e-04  -1.515
## VTRatio_elite:vowel.paira-i            5.680e+01  6.933e+00   8.193
## VTRatio_elite:vowel.paira-schwa       -3.343e+01  6.933e+00  -4.823
## VTRatio_elite:vowel.paira-u           -1.917e+01  6.933e+00  -2.765
## VTRatio_elite:vowel.pairae-i           2.843e+01  6.933e+00   4.100
## VTRatio_elite:vowel.pairae-schwa       4.748e+00  6.933e+00   0.685
## VTRatio_elite:vowel.pairae-u           4.551e+01  6.933e+00   6.564
## VTRatio_elite:vowel.pairi-schwa        4.174e+01  6.933e+00   6.021
## VTRatio_elite:vowel.pairi-u            9.290e+01  6.933e+00  13.401
## VTRatio_elite:vowel.pairschwa-u       -3.293e+01  6.933e+00  -4.750
## I(VTRatio_elite^2):vowel.paira-i      -5.992e+01  7.608e+00  -7.876
## I(VTRatio_elite^2):vowel.paira-schwa   3.397e+01  7.608e+00   4.465
## I(VTRatio_elite^2):vowel.paira-u       1.193e+01  7.608e+00   1.568
## I(VTRatio_elite^2):vowel.pairae-i     -3.197e+01  7.608e+00  -4.202
## I(VTRatio_elite^2):vowel.pairae-schwa -4.652e+00  7.608e+00  -0.612
## I(VTRatio_elite^2):vowel.pairae-u     -5.460e+01  7.608e+00  -7.176
## I(VTRatio_elite^2):vowel.pairi-schwa  -4.297e+01  7.608e+00  -5.648
## I(VTRatio_elite^2):vowel.pairi-u      -9.978e+01  7.608e+00 -13.115
## I(VTRatio_elite^2):vowel.pairschwa-u   2.786e+01  7.608e+00   3.662
##                                       Pr(>|t|)    
## (Intercept)                            < 2e-16 ***
## VTRatio_elite                          < 2e-16 ***
## I(VTRatio_elite^2)                     < 2e-16 ***
## vowel.paira-i                         1.28e-10 ***
## vowel.paira-schwa                     5.16e-05 ***
## vowel.paira-u                         1.39e-06 ***
## vowel.pairae-i                        0.001201 ** 
## vowel.pairae-schwa                    0.230733    
## vowel.pairae-u                        0.001193 ** 
## vowel.pairi-schwa                     1.08e-07 ***
## vowel.pairi-u                          < 2e-16 ***
## vowel.pairschwa-u                     1.27e-11 ***
## replication                           0.129945    
## VTRatio_elite:vowel.paira-i           3.10e-16 ***
## VTRatio_elite:vowel.paira-schwa       1.45e-06 ***
## VTRatio_elite:vowel.paira-u           0.005717 ** 
## VTRatio_elite:vowel.pairae-i          4.18e-05 ***
## VTRatio_elite:vowel.pairae-schwa      0.493416    
## VTRatio_elite:vowel.pairae-u          5.66e-11 ***
## VTRatio_elite:vowel.pairi-schwa       1.83e-09 ***
## VTRatio_elite:vowel.pairi-u            < 2e-16 ***
## VTRatio_elite:vowel.pairschwa-u       2.08e-06 ***
## I(VTRatio_elite^2):vowel.paira-i      3.97e-15 ***
## I(VTRatio_elite^2):vowel.paira-schwa  8.17e-06 ***
## I(VTRatio_elite^2):vowel.paira-u      0.116988    
## I(VTRatio_elite^2):vowel.pairae-i     2.68e-05 ***
## I(VTRatio_elite^2):vowel.pairae-schwa 0.540867    
## I(VTRatio_elite^2):vowel.pairae-u     8.03e-13 ***
## I(VTRatio_elite^2):vowel.pairi-schwa  1.70e-08 ***
## I(VTRatio_elite^2):vowel.pairi-u       < 2e-16 ***
## I(VTRatio_elite^2):vowel.pairschwa-u  0.000252 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2254 on 5969 degrees of freedom
## Multiple R-squared:  0.9881, Adjusted R-squared:  0.9881 
## F-statistic: 1.657e+04 on 30 and 5969 DF,  p-value: < 2.2e-16

F1–F2

##                                 Df Sum Sq Mean Sq  F value Pr(>F)    
## VTRatio_elite                    1     49    48.7  1120.54 <2e-16 ***
## I(VTRatio_elite^2)               1    154   154.4  3555.45 <2e-16 ***
## vowel.pair                       9  24620  2735.5 62990.14 <2e-16 ***
## replication                      1      0     0.2     4.22   0.04 *  
## VTRatio_elite:vowel.pair         9    157    17.5   402.49 <2e-16 ***
## I(VTRatio_elite^2):vowel.pair    9     35     3.9    88.82 <2e-16 ***
## Residuals                     5969    259     0.0                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = ive12.lm)
## 
## $vowel.pair
##                        diff         lwr        upr p adj
## a-i-a-ae          3.1454271  3.10734850  3.1835057     0
## a-schwa-a-ae     -1.8238912 -1.86196986 -1.7858126     0
## a-u-a-ae          1.2563157  1.21823712  1.2943944     0
## ae-i-a-ae         1.0623131  1.02423452  1.1003918     0
## ae-schwa-a-ae    -0.6905142 -0.72859279 -0.6524356     0
## ae-u-a-ae         4.1640962  4.12601760  4.2021748     0
## i-schwa-a-ae      1.5362092  1.49813059  1.5742878     0
## i-u-a-ae          5.0867498  5.04867123  5.1248285     0
## schwa-u-a-ae      1.3753741  1.33729551  1.4134527     0
## a-schwa-a-i      -4.9693184 -5.00739698 -4.9312397     0
## a-u-a-i          -1.8891114 -1.92719001 -1.8510328     0
## ae-i-a-i         -2.0831140 -2.12119260 -2.0450354     0
## ae-schwa-a-i     -3.8359413 -3.87401992 -3.7978627     0
## ae-u-a-i          1.0186691  0.98059047  1.0567477     0
## i-schwa-a-i      -1.6092179 -1.64729654 -1.5711393     0
## i-u-a-i           1.9413227  1.90324410  1.9794013     0
## schwa-u-a-i      -1.7700530 -1.80813162 -1.7319744     0
## a-u-a-schwa       3.0802070  3.04212836  3.1182856     0
## ae-i-a-schwa      2.8862044  2.84812576  2.9242830     0
## ae-schwa-a-schwa  1.1333771  1.09529844  1.1714557     0
## ae-u-a-schwa      5.9879875  5.94990883  6.0260661     0
## i-schwa-a-schwa   3.3601004  3.32202183  3.3981791     0
## i-u-a-schwa       6.9106411  6.87256246  6.9487197     0
## schwa-u-a-schwa   3.1992654  3.16118674  3.2373440     0
## ae-i-a-u         -0.1940026 -0.23208122 -0.1559240     0
## ae-schwa-a-u     -1.9468299 -1.98490853 -1.9087513     0
## ae-u-a-u          2.9077805  2.86970186  2.9458591     0
## i-schwa-a-u       0.2798935  0.24181485  0.3179721     0
## i-u-a-u           3.8304341  3.79235549  3.8685127     0
## schwa-u-a-u       0.1190584  0.08097977  0.1571370     0
## ae-schwa-ae-i    -1.7528273 -1.79090594 -1.7147487     0
## ae-u-ae-i         3.1017831  3.06370445  3.1398617     0
## i-schwa-ae-i      0.4738961  0.43581745  0.5119747     0
## i-u-ae-i          4.0244367  3.98635808  4.0625153     0
## schwa-u-ae-i      0.3130610  0.27498236  0.3511396     0
## ae-u-ae-schwa     4.8546104  4.81653177  4.8926890     0
## i-schwa-ae-schwa  2.2267234  2.18864476  2.2648020     0
## i-u-ae-schwa      5.7772640  5.73918540  5.8153426     0
## schwa-u-ae-schwa  2.0658883  2.02780968  2.1039669     0
## i-schwa-ae-u     -2.6278870 -2.66596563 -2.5898084     0
## i-u-ae-u          0.9226536  0.88457501  0.9607323     0
## schwa-u-ae-u     -2.7887221 -2.82680071 -2.7506435     0
## i-u-i-schwa       3.5505406  3.51246202  3.5886193     0
## schwa-u-i-schwa  -0.1608351 -0.19891370 -0.1227565     0
## schwa-u-i-u      -3.7113757 -3.74945434 -3.6732971     0
## 
## Call:
## lm(formula = dist_elite_F1F2 ~ VTRatio_elite + I(VTRatio_elite^2) + 
##     vowel.pair + (VTRatio_elite:vowel.pair) + (I(VTRatio_elite^2):vowel.pair) + 
##     replication, data = intervowel.dists[intervowel.dists$fixed.hyoid == 
##     FALSE, ])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.65321 -0.07894  0.01856  0.10477  1.11594 
## 
## Coefficients:
##                                         Estimate Std. Error t value
## (Intercept)                           -9.654e+00  1.025e+00  -9.420
## VTRatio_elite                          5.543e+01  4.533e+00  12.229
## I(VTRatio_elite^2)                    -5.773e+01  4.974e+00 -11.606
## vowel.paira-i                         -1.715e+01  1.449e+00 -11.832
## vowel.paira-schwa                      6.031e+00  1.449e+00   4.161
## vowel.paira-u                          2.819e+00  1.449e+00   1.945
## vowel.pairae-i                        -1.127e+01  1.449e+00  -7.778
## vowel.pairae-schwa                    -3.437e+00  1.449e+00  -2.372
## vowel.pairae-u                        -6.561e+00  1.449e+00  -4.527
## vowel.pairi-schwa                     -1.447e+01  1.449e+00  -9.983
## vowel.pairi-u                         -1.783e+01  1.449e+00 -12.303
## vowel.pairschwa-u                      6.730e+00  1.449e+00   4.643
## replication                           -1.914e-04  9.320e-05  -2.054
## VTRatio_elite:vowel.paira-i            8.645e+01  6.411e+00  13.486
## VTRatio_elite:vowel.paira-schwa       -3.246e+01  6.411e+00  -5.063
## VTRatio_elite:vowel.paira-u           -3.328e-02  6.411e+00  -0.005
## VTRatio_elite:vowel.pairae-i           5.419e+01  6.411e+00   8.453
## VTRatio_elite:vowel.pairae-schwa       1.161e+01  6.411e+00   1.812
## VTRatio_elite:vowel.pairae-u           5.096e+01  6.411e+00   7.949
## VTRatio_elite:vowel.pairi-schwa        6.752e+01  6.411e+00  10.532
## VTRatio_elite:vowel.pairi-u            9.871e+01  6.411e+00  15.397
## VTRatio_elite:vowel.pairschwa-u       -1.699e+01  6.411e+00  -2.651
## I(VTRatio_elite^2):vowel.paira-i      -9.109e+01  7.035e+00 -12.948
## I(VTRatio_elite^2):vowel.paira-schwa   3.305e+01  7.035e+00   4.699
## I(VTRatio_elite^2):vowel.paira-u      -7.471e+00  7.035e+00  -1.062
## I(VTRatio_elite^2):vowel.pairae-i     -5.895e+01  7.035e+00  -8.380
## I(VTRatio_elite^2):vowel.pairae-schwa -1.214e+01  7.035e+00  -1.726
## I(VTRatio_elite^2):vowel.pairae-u     -5.966e+01  7.035e+00  -8.481
## I(VTRatio_elite^2):vowel.pairi-schwa  -7.039e+01  7.035e+00 -10.006
## I(VTRatio_elite^2):vowel.pairi-u      -1.052e+02  7.035e+00 -14.956
## I(VTRatio_elite^2):vowel.pairschwa-u   1.131e+01  7.035e+00   1.608
##                                       Pr(>|t|)    
## (Intercept)                            < 2e-16 ***
## VTRatio_elite                          < 2e-16 ***
## I(VTRatio_elite^2)                     < 2e-16 ***
## vowel.paira-i                          < 2e-16 ***
## vowel.paira-schwa                     3.21e-05 ***
## vowel.paira-u                          0.05180 .  
## vowel.pairae-i                        8.65e-15 ***
## vowel.pairae-schwa                     0.01775 *  
## vowel.pairae-u                        6.10e-06 ***
## vowel.pairi-schwa                      < 2e-16 ***
## vowel.pairi-u                          < 2e-16 ***
## vowel.pairschwa-u                     3.50e-06 ***
## replication                            0.04000 *  
## VTRatio_elite:vowel.paira-i            < 2e-16 ***
## VTRatio_elite:vowel.paira-schwa       4.25e-07 ***
## VTRatio_elite:vowel.paira-u            0.99586    
## VTRatio_elite:vowel.pairae-i           < 2e-16 ***
## VTRatio_elite:vowel.pairae-schwa       0.07006 .  
## VTRatio_elite:vowel.pairae-u          2.23e-15 ***
## VTRatio_elite:vowel.pairi-schwa        < 2e-16 ***
## VTRatio_elite:vowel.pairi-u            < 2e-16 ***
## VTRatio_elite:vowel.pairschwa-u        0.00806 ** 
## I(VTRatio_elite^2):vowel.paira-i       < 2e-16 ***
## I(VTRatio_elite^2):vowel.paira-schwa  2.68e-06 ***
## I(VTRatio_elite^2):vowel.paira-u       0.28831    
## I(VTRatio_elite^2):vowel.pairae-i      < 2e-16 ***
## I(VTRatio_elite^2):vowel.pairae-schwa  0.08446 .  
## I(VTRatio_elite^2):vowel.pairae-u      < 2e-16 ***
## I(VTRatio_elite^2):vowel.pairi-schwa   < 2e-16 ***
## I(VTRatio_elite^2):vowel.pairi-u       < 2e-16 ***
## I(VTRatio_elite^2):vowel.pairschwa-u   0.10791    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2084 on 5969 degrees of freedom
## Multiple R-squared:  0.9897, Adjusted R-squared:  0.9897 
## F-statistic: 1.92e+04 on 30 and 5969 DF,  p-value: < 2.2e-16

Summarized

Summary of intervowel distance regressions with betas (for non-factor DVs and ‘.’ for factors), p-values, and adjusted R2. Interactions are denoted by ‘:’.
DVs, interactions & R2 Dist(F1-F5) Dist(F1-F2)
VTRatio_elite 54 (1.8e-27***) 55 (5.6e-34***)
VTRatio_elite^2 -55 (1e-24***) -58 (8.2e-31***)
vowel.pair . (0***) . (0***)
replication -0.00015 (0.13) -0.00019 (0.04*)
VTRatio_elite:vowel.pair . (0***) . (0***)
VTRatio_elite^2:vowel.pair . (1.5e-112***) . (8.8e-156***)
adjusted R2 98.8% 99.0%
Predicted intervowel distances with 95% prediction intervals function of VTRatio per vowel pair.

Predicted intervowel distances with 95% prediction intervals function of VTRatio per vowel pair.

Raw intervowel distance (F1-F5) function of VTRatio per vowel pair.

Raw intervowel distance (F1-F5) function of VTRatio per vowel pair.

Target-elite Procrustes distances

## 
## Call:
## lm(formula = Proc.rmsd ~ VTRatio_elite + I(VTRatio_elite^2) + 
##     replication, data = tmp)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.28666 -0.05387 -0.01242  0.04205  0.44509 
## 
## Coefficients:
##                      Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         1.115e+01  4.772e-01  23.359   <2e-16 ***
## VTRatio_elite      -4.816e+01  2.110e+00 -22.820   <2e-16 ***
## I(VTRatio_elite^2)  5.260e+01  2.316e+00  22.713   <2e-16 ***
## replication         9.578e-05  1.372e-04   0.698    0.485    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.09702 on 596 degrees of freedom
## Multiple R-squared:  0.4686, Adjusted R-squared:  0.4659 
## F-statistic: 175.2 on 3 and 596 DF,  p-value: < 2.2e-16
Summary of Procrustes distance regression (for non-factor DVs and ‘.’ for factors), p-values, and adjusted R2. Interactions are denoted by ‘:’.
DVs, interactions & R2 Procr.dist
VTRatio_elite -48 (2.6e-83***)
VTRatio_elite^2 53 (9.5e-83***)
replication 9.6e-05 (0.49)
adjusted R2 46.6%

Principal Component Analysis

PCA acoustics & articulation

Mobile hyoid
PCA of articulatory and acoustic parameters for the mobile hyoid.

PCA of articulatory and acoustic parameters for the mobile hyoid.

PCA on acoustics only for the mobile hyoid.

PCA on acoustics only for the mobile hyoid.

The first three PCs explain together 60.7% of the variance:

  • PC1 explains 27.2% of variance;
  • PC2 explains 17.3% of variance;
  • PC3 explains 16.2% of variance.

Stats (mobile hyoid only)

Acoustics on VTRatio and articulatory parameters

F1

##                      Df Sum Sq Mean Sq   F value   Pr(>F)    
## VTRatio               1     47    47.0 6.080e+03  < 2e-16 ***
## I(VTRatio^2)          1      1     1.1 1.465e+02  < 2e-16 ***
## vowel                 4   8870  2217.5 2.866e+05  < 2e-16 ***
## JA                    1      1     1.2 1.487e+02  < 2e-16 ***
## LP                    1      3     3.4 4.361e+02  < 2e-16 ***
## LD                    1      1     1.4 1.786e+02  < 2e-16 ***
## TCX                   1      4     4.2 5.468e+02  < 2e-16 ***
## TCY                   1      6     6.4 8.311e+02  < 2e-16 ***
## TTX                   1      0     0.0 2.900e-02   0.8638    
## TTY                   1      2     2.4 3.134e+02  < 2e-16 ***
## TBX                   1      0     0.0 5.837e+00   0.0158 *  
## TBY                   1      0     0.3 3.962e+01 3.55e-10 ***
## hyoidX                1      0     0.3 3.736e+01 1.11e-09 ***
## hyoidY                1      0     0.0 1.748e+00   0.1862    
## replication           1      0     0.0 2.007e+00   0.1567    
## generation            1      1     1.3 1.672e+02  < 2e-16 ***
## VTRatio:vowel         4      6     1.5 1.961e+02  < 2e-16 ***
## I(VTRatio^2):vowel    4      7     1.7 2.170e+02  < 2e-16 ***
## vowel:JA              4      1     0.4 4.769e+01  < 2e-16 ***
## vowel:LP              4      2     0.5 6.612e+01  < 2e-16 ***
## vowel:LD              4      1     0.2 2.673e+01  < 2e-16 ***
## vowel:TCX             4      3     0.7 8.829e+01  < 2e-16 ***
## vowel:TCY             4      1     0.1 1.647e+01 2.38e-13 ***
## vowel:TTX             4      1     0.4 4.559e+01  < 2e-16 ***
## vowel:TTY             4      0     0.0 6.010e+00 8.17e-05 ***
## vowel:TBX             4      2     0.5 6.681e+01  < 2e-16 ***
## vowel:TBY             4      2     0.6 7.423e+01  < 2e-16 ***
## vowel:hyoidX          4      1     0.3 3.458e+01  < 2e-16 ***
## vowel:hyoidY          4      0     0.1 1.329e+01 9.90e-11 ***
## Residuals          2928     23     0.0                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f1.m0)
## 
## $vowel
##                diff        lwr        upr p adj
## a-schwa   1.2653481  1.2514864  1.2792097     0
## ae-schwa  1.4167198  1.4028581  1.4305814     0
## i-schwa  -2.7417014 -2.7555630 -2.7278397     0
## u-schwa  -2.1471948 -2.1610565 -2.1333332     0
## ae-a      0.1513717  0.1375101  0.1652333     0
## i-a      -4.0070494 -4.0209111 -3.9931878     0
## u-a      -3.4125429 -3.4264046 -3.3986813     0
## i-ae     -4.1584211 -4.1722828 -4.1445595     0
## u-ae     -3.5639146 -3.5777763 -3.5500530     0
## u-i       0.5945065  0.5806449  0.6083681     0
## 
## Call:
## lm(formula = F1 ~ VTRatio + I(VTRatio^2) + vowel + JA + LP + 
##     LD + TCX + TCY + TTX + TTY + TBX + TBY + hyoidX + hyoidY + 
##     (VTRatio:vowel) + (I(VTRatio^2):vowel) + (JA:vowel) + (LP:vowel) + 
##     (LD:vowel) + (TCX:vowel) + (TCY:vowel) + (TTX:vowel) + (TTY:vowel) + 
##     (TBX:vowel) + (TBY:vowel) + (hyoidX:vowel) + (hyoidY:vowel) + 
##     replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.70734 -0.03794  0.00437  0.03917  0.80442 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           2.534e+00  1.010e+00   2.508 0.012194 *  
## VTRatio               1.032e+01  3.671e+00   2.810 0.004982 ** 
## I(VTRatio^2)         -1.086e+01  3.703e+00  -2.933 0.003382 ** 
## vowela               -5.085e-01  1.312e+00  -0.388 0.698356    
## vowelae              -1.119e+01  1.417e+00  -7.900 3.93e-15 ***
## voweli                3.437e+00  1.276e+00   2.693 0.007118 ** 
## vowelu                4.277e+00  1.211e+00   3.532 0.000419 ***
## JA                    9.673e-04  2.512e-03   0.385 0.700169    
## LP                    6.779e-03  9.024e-03   0.751 0.452610    
## LD                    1.499e-03  4.309e-03   0.348 0.728025    
## TCX                  -1.322e-02  1.587e-02  -0.833 0.405011    
## TCY                  -3.485e-03  1.003e-02  -0.348 0.728209    
## TTX                  -4.840e-03  5.372e-03  -0.901 0.367676    
## TTY                   7.859e-04  4.850e-03   0.162 0.871268    
## TBX                   4.546e-03  2.681e-03   1.696 0.090025 .  
## TBY                   4.324e-04  4.681e-03   0.092 0.926398    
## hyoidX               -1.779e-02  9.642e-03  -1.845 0.065106 .  
## hyoidY               -3.660e-02  2.858e-02  -1.281 0.200338    
## replication           1.375e-05  5.604e-05   0.245 0.806166    
## generation           -1.363e-04  1.897e-05  -7.188 8.32e-13 ***
## VTRatio:vowela        8.029e+00  4.783e+00   1.679 0.093342 .  
## VTRatio:vowelae       5.414e+01  5.177e+00  10.459  < 2e-16 ***
## VTRatio:voweli       -2.407e+01  4.753e+00  -5.064 4.36e-07 ***
## VTRatio:vowelu       -2.817e+01  4.343e+00  -6.487 1.02e-10 ***
## I(VTRatio^2):vowela  -7.485e+00  4.909e+00  -1.525 0.127404    
## I(VTRatio^2):vowelae -5.662e+01  5.318e+00 -10.646  < 2e-16 ***
## I(VTRatio^2):voweli   2.692e+01  4.886e+00   5.510 3.91e-08 ***
## I(VTRatio^2):vowelu   3.413e+01  4.383e+00   7.786 9.50e-15 ***
## vowela:JA            -1.336e-02  4.653e-03  -2.872 0.004114 ** 
## vowelae:JA            3.495e-03  6.508e-03   0.537 0.591317    
## voweli:JA            -4.632e-04  3.896e-03  -0.119 0.905377    
## vowelu:JA             7.349e-03  3.174e-03   2.315 0.020683 *  
## vowela:LP            -2.423e-02  1.418e-02  -1.709 0.087480 .  
## vowelae:LP           -1.695e-02  1.661e-02  -1.021 0.307548    
## voweli:LP            -1.915e-02  1.221e-02  -1.569 0.116863    
## vowelu:LP            -1.560e-01  1.182e-02 -13.204  < 2e-16 ***
## vowela:LD            -7.858e-05  6.847e-03  -0.011 0.990844    
## vowelae:LD           -1.537e-02  7.418e-03  -2.072 0.038360 *  
## voweli:LD            -4.784e-04  5.660e-03  -0.085 0.932635    
## vowelu:LD             5.340e-02  6.636e-03   8.047 1.22e-15 ***
## vowela:TCX           -6.135e-02  4.802e-02  -1.278 0.201475    
## vowelae:TCX          -1.101e-01  2.473e-02  -4.453 8.78e-06 ***
## voweli:TCX           -4.136e-02  1.682e-02  -2.459 0.013988 *  
## vowelu:TCX           -3.402e-01  2.161e-02 -15.741  < 2e-16 ***
## vowela:TCY           -1.578e-01  3.042e-02  -5.186 2.29e-07 ***
## vowelae:TCY          -1.091e-02  2.005e-02  -0.544 0.586390    
## voweli:TCY           -5.283e-02  1.710e-02  -3.090 0.002022 ** 
## vowelu:TCY            9.311e-02  1.617e-02   5.758 9.41e-09 ***
## vowela:TTX           -2.164e-02  8.122e-03  -2.664 0.007764 ** 
## vowelae:TTX          -4.318e-03  7.840e-03  -0.551 0.581850    
## voweli:TTX            1.074e-02  6.657e-03   1.613 0.106841    
## vowelu:TTX            9.265e-02  7.562e-03  12.253  < 2e-16 ***
## vowela:TTY           -8.013e-02  8.657e-03  -9.256  < 2e-16 ***
## vowelae:TTY          -5.741e-02  1.218e-02  -4.713 2.55e-06 ***
## voweli:TTY           -1.750e-02  7.298e-03  -2.398 0.016546 *  
## vowelu:TTY           -4.441e-03  6.481e-03  -0.685 0.493236    
## vowela:TBX           -9.160e-03  4.596e-03  -1.993 0.046352 *  
## vowelae:TBX           1.594e-03  7.319e-03   0.218 0.827653    
## voweli:TBX           -4.741e-02  7.053e-03  -6.722 2.15e-11 ***
## vowelu:TBX           -5.896e-03  5.303e-03  -1.112 0.266278    
## vowela:TBY           -1.120e-01  7.901e-03 -14.174  < 2e-16 ***
## vowelae:TBY          -8.468e-02  1.354e-02  -6.256 4.52e-10 ***
## voweli:TBY           -1.803e-02  1.345e-02  -1.340 0.180245    
## vowelu:TBY            3.838e-02  7.972e-03   4.815 1.55e-06 ***
## vowela:hyoidX        -2.151e-01  1.928e-02 -11.155  < 2e-16 ***
## vowelae:hyoidX       -1.744e-02  1.827e-02  -0.955 0.339778    
## voweli:hyoidX         2.438e-02  1.599e-02   1.525 0.127463    
## vowelu:hyoidX        -3.959e-02  1.406e-02  -2.817 0.004884 ** 
## vowela:hyoidY         2.600e-01  4.156e-02   6.256 4.54e-10 ***
## vowelae:hyoidY        3.164e-02  4.587e-02   0.690 0.490352    
## voweli:hyoidY         1.478e-01  4.109e-02   3.597 0.000327 ***
## vowelu:hyoidY         1.967e-01  3.931e-02   5.005 5.93e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.08796 on 2928 degrees of freedom
## Multiple R-squared:  0.9975, Adjusted R-squared:  0.9974 
## F-statistic: 1.632e+04 on 71 and 2928 DF,  p-value: < 2.2e-16
##                      Df Sum Sq Mean Sq F value   Pr(>F)    
## VTRatio               1  0.563  0.5629  58.177 3.22e-14 ***
## I(VTRatio^2)          1  2.569  2.5685 265.447  < 2e-16 ***
## vowel                 4  5.657  1.4142 146.147  < 2e-16 ***
## JA                    1  0.245  0.2447  25.290 5.23e-07 ***
## LP                    1  0.798  0.7977  82.444  < 2e-16 ***
## LD                    1  0.295  0.2948  30.469 3.69e-08 ***
## TCX                   1  0.590  0.5901  60.981 7.97e-15 ***
## TCY                   1  0.407  0.4070  42.058 1.04e-10 ***
## TTX                   1  0.117  0.1174  12.136 0.000502 ***
## TTY                   1  1.364  1.3639 140.954  < 2e-16 ***
## TBX                   1  0.405  0.4052  41.875 1.14e-10 ***
## TBY                   1  0.037  0.0373   3.858 0.049601 *  
## hyoidX                1  0.006  0.0059   0.607 0.435905    
## hyoidY                1  0.493  0.4931  50.962 1.18e-12 ***
## replication           1  0.037  0.0371   3.839 0.050177 .  
## generation            1  0.994  0.9944 102.765  < 2e-16 ***
## VTRatio:vowel         4  9.100  2.2750 235.116  < 2e-16 ***
## I(VTRatio^2):vowel    4  1.820  0.4550  47.019  < 2e-16 ***
## vowel:JA              4  0.777  0.1943  20.084 2.47e-16 ***
## vowel:LP              4  1.210  0.3024  31.251  < 2e-16 ***
## vowel:LD              4  0.397  0.0993  10.266 2.97e-08 ***
## vowel:TCX             4  5.183  1.2958 133.915  < 2e-16 ***
## vowel:TCY             4  0.260  0.0650   6.712 2.25e-05 ***
## vowel:TTX             4  0.995  0.2488  25.715  < 2e-16 ***
## vowel:TTY             4  0.183  0.0456   4.715 0.000858 ***
## vowel:TBX             4  0.180  0.0451   4.662 0.000944 ***
## vowel:TBY             4  0.414  0.1034  10.687 1.34e-08 ***
## vowel:hyoidX          4  0.189  0.0473   4.889 0.000627 ***
## vowel:hyoidY          4  0.255  0.0638   6.594 2.79e-05 ***
## Residuals          2928 28.332  0.0097                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f1e.m0)
## 
## $vowel
##                  diff         lwr          upr     p adj
## a-schwa   0.056413580  0.04091216  0.071915002 0.0000000
## ae-schwa  0.050095389  0.03459397  0.065596811 0.0000000
## i-schwa   0.025828249  0.01032683  0.041329671 0.0000553
## u-schwa   0.129513906  0.11401248  0.145015328 0.0000000
## ae-a     -0.006318191 -0.02181961  0.009183231 0.8000321
## i-a      -0.030585331 -0.04608675 -0.015083909 0.0000008
## u-a       0.073100326  0.05759890  0.088601748 0.0000000
## i-ae     -0.024267140 -0.03976856 -0.008765718 0.0001932
## u-ae      0.079418517  0.06391709  0.094919939 0.0000000
## u-i       0.103685656  0.08818423  0.119187079 0.0000000
## 
## Call:
## lm(formula = F1.error ~ VTRatio + I(VTRatio^2) + vowel + JA + 
##     LP + LD + TCX + TCY + TTX + TTY + TBX + TBY + hyoidX + hyoidY + 
##     (VTRatio:vowel) + (I(VTRatio^2):vowel) + (JA:vowel) + (LP:vowel) + 
##     (LD:vowel) + (TCX:vowel) + (TCY:vowel) + (TTX:vowel) + (TTY:vowel) + 
##     (TBX:vowel) + (TBY:vowel) + (hyoidX:vowel) + (hyoidY:vowel) + 
##     replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.52699 -0.02280 -0.00312  0.01594  2.09411 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           8.280e-01  1.130e+00   0.733 0.463759    
## VTRatio              -3.602e+00  4.105e+00  -0.877 0.380408    
## I(VTRatio^2)          4.001e+00  4.141e+00   0.966 0.333955    
## vowela                1.603e+00  1.467e+00   1.093 0.274698    
## vowelae               7.255e+00  1.584e+00   4.579 4.86e-06 ***
## voweli                1.592e+00  1.427e+00   1.116 0.264581    
## vowelu                6.268e+00  1.354e+00   4.628 3.84e-06 ***
## JA                   -2.292e-03  2.809e-03  -0.816 0.414495    
## LP                    1.476e-03  1.009e-02   0.146 0.883710    
## LD                    4.393e-04  4.819e-03   0.091 0.927372    
## TCX                   3.532e-03  1.775e-02   0.199 0.842271    
## TCY                  -2.631e-03  1.121e-02  -0.235 0.814516    
## TTX                  -2.072e-03  6.007e-03  -0.345 0.730230    
## TTY                  -1.847e-03  5.423e-03  -0.341 0.733395    
## TBX                   3.152e-04  2.998e-03   0.105 0.916262    
## TBY                   9.597e-04  5.234e-03   0.183 0.854549    
## hyoidX               -9.548e-03  1.078e-02  -0.886 0.375945    
## hyoidY                4.029e-03  3.196e-02   0.126 0.899681    
## replication           7.903e-05  6.267e-05   1.261 0.207382    
## generation           -1.561e-04  2.121e-05  -7.361 2.36e-13 ***
## VTRatio:vowela       -7.301e+00  5.349e+00  -1.365 0.172363    
## VTRatio:vowelae      -2.863e+01  5.789e+00  -4.946 8.02e-07 ***
## VTRatio:voweli       -5.357e+00  5.315e+00  -1.008 0.313546    
## VTRatio:vowelu       -2.876e+01  4.857e+00  -5.922 3.55e-09 ***
## I(VTRatio^2):vowela   7.713e+00  5.490e+00   1.405 0.160105    
## I(VTRatio^2):vowelae  2.876e+01  5.947e+00   4.836 1.39e-06 ***
## I(VTRatio^2):voweli   5.596e+00  5.464e+00   1.024 0.305862    
## I(VTRatio^2):vowelu   3.519e+01  4.901e+00   7.180 8.79e-13 ***
## vowela:JA             8.298e-03  5.203e-03   1.595 0.110895    
## vowelae:JA            4.407e-03  7.278e-03   0.606 0.544856    
## voweli:JA             4.828e-03  4.357e-03   1.108 0.267921    
## vowelu:JA             5.851e-03  3.550e-03   1.648 0.099418 .  
## vowela:LP             2.845e-02  1.585e-02   1.795 0.072835 .  
## vowelae:LP            8.311e-03  1.857e-02   0.447 0.654578    
## voweli:LP            -1.873e-03  1.365e-02  -0.137 0.890897    
## vowelu:LP            -1.037e-01  1.321e-02  -7.850 5.81e-15 ***
## vowela:LD            -4.060e-03  7.657e-03  -0.530 0.596024    
## vowelae:LD            8.854e-03  8.296e-03   1.067 0.285949    
## voweli:LD            -2.712e-04  6.329e-03  -0.043 0.965830    
## vowelu:LD             3.558e-02  7.421e-03   4.794 1.72e-06 ***
## vowela:TCX            3.276e-03  5.370e-02   0.061 0.951356    
## vowelae:TCX           1.379e-02  2.765e-02   0.499 0.617956    
## voweli:TCX           -1.578e-02  1.881e-02  -0.839 0.401459    
## vowelu:TCX           -3.674e-01  2.417e-02 -15.201  < 2e-16 ***
## vowela:TCY            3.661e-02  3.402e-02   1.076 0.282035    
## vowelae:TCY           3.173e-02  2.243e-02   1.415 0.157258    
## voweli:TCY           -1.905e-02  1.912e-02  -0.996 0.319344    
## vowelu:TCY            1.056e-01  1.808e-02   5.842 5.73e-09 ***
## vowela:TTX            9.985e-03  9.082e-03   1.099 0.271705    
## vowelae:TTX          -4.223e-03  8.767e-03  -0.482 0.630076    
## voweli:TTX            1.586e-03  7.444e-03   0.213 0.831257    
## vowelu:TTX            6.627e-02  8.456e-03   7.837 6.41e-15 ***
## vowela:TTY            4.718e-02  9.681e-03   4.873 1.16e-06 ***
## vowelae:TTY           3.178e-02  1.362e-02   2.333 0.019731 *  
## voweli:TTY            1.274e-03  8.161e-03   0.156 0.875971    
## vowelu:TTY           -6.956e-03  7.247e-03  -0.960 0.337189    
## vowela:TBX            4.157e-04  5.140e-03   0.081 0.935546    
## vowelae:TBX          -1.303e-02  8.185e-03  -1.592 0.111598    
## voweli:TBX           -8.674e-03  7.888e-03  -1.100 0.271553    
## vowelu:TBX            6.771e-03  5.930e-03   1.142 0.253685    
## vowela:TBY            6.228e-02  8.836e-03   7.048 2.25e-12 ***
## vowelae:TBY           3.118e-02  1.514e-02   2.060 0.039494 *  
## voweli:TBY           -2.266e-03  1.504e-02  -0.151 0.880251    
## vowelu:TBY            3.194e-02  8.915e-03   3.582 0.000346 ***
## vowela:hyoidX         1.027e-01  2.156e-02   4.764 1.99e-06 ***
## vowelae:hyoidX        1.224e-02  2.043e-02   0.599 0.549116    
## voweli:hyoidX         8.159e-03  1.788e-02   0.456 0.648247    
## vowelu:hyoidX        -9.199e-03  1.572e-02  -0.585 0.558435    
## vowela:hyoidY        -1.131e-01  4.648e-02  -2.433 0.015020 *  
## vowelae:hyoidY        1.014e-02  5.129e-02   0.198 0.843277    
## voweli:hyoidY         5.323e-02  4.595e-02   1.158 0.246782    
## vowelu:hyoidY         1.124e-01  4.396e-02   2.556 0.010638 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.09837 on 2928 degrees of freedom
## Multiple R-squared:  0.5564, Adjusted R-squared:  0.5457 
## F-statistic: 51.73 on 71 and 2928 DF,  p-value: < 2.2e-16

F2

##                      Df Sum Sq Mean Sq   F value   Pr(>F)    
## VTRatio               1    104     104 6.194e+03  < 2e-16 ***
## I(VTRatio^2)          1     34      34 2.028e+03  < 2e-16 ***
## vowel                 4  25849    6462 3.846e+05  < 2e-16 ***
## JA                    1      1       1 6.363e+01 2.13e-15 ***
## LP                    1      0       0 1.315e+01 0.000292 ***
## LD                    1      0       0 1.160e+01 0.000669 ***
## TCX                   1     14      14 8.529e+02  < 2e-16 ***
## TCY                   1     15      15 8.940e+02  < 2e-16 ***
## TTX                   1      2       2 9.240e+01  < 2e-16 ***
## TTY                   1      2       2 1.054e+02  < 2e-16 ***
## TBX                   1      0       0 4.973e+00 0.025814 *  
## TBY                   1      1       1 8.053e+01  < 2e-16 ***
## hyoidX                1      3       3 1.919e+02  < 2e-16 ***
## hyoidY                1      2       2 1.385e+02  < 2e-16 ***
## replication           1      0       0 8.900e-02 0.765604    
## generation            1      1       1 5.340e+01 3.49e-13 ***
## VTRatio:vowel         4     26       7 3.883e+02  < 2e-16 ***
## I(VTRatio^2):vowel    4     25       6 3.794e+02  < 2e-16 ***
## vowel:JA              4      1       0 1.667e+01 1.62e-13 ***
## vowel:LP              4      0       0 5.943e+00 9.23e-05 ***
## vowel:LD              4      1       0 1.400e+01 2.57e-11 ***
## vowel:TCX             4      3       1 4.377e+01  < 2e-16 ***
## vowel:TCY             4      3       1 4.619e+01  < 2e-16 ***
## vowel:TTX             4      0       0 1.424e+00 0.223314    
## vowel:TTY             4      1       0 1.919e+01 1.34e-15 ***
## vowel:TBX             4      1       0 9.479e+00 1.30e-07 ***
## vowel:TBY             4      0       0 2.685e+00 0.029822 *  
## vowel:hyoidX          4      1       0 1.186e+01 1.47e-09 ***
## vowel:hyoidY          4      2       0 2.333e+01  < 2e-16 ***
## Residuals          2928     49       0                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f2.m0)
## 
## $vowel
##               diff       lwr       upr p adj
## a-schwa  -1.082595 -1.103023 -1.062167     0
## ae-schwa  2.376443  2.356015  2.396871     0
## i-schwa   4.193568  4.173140  4.213996     0
## u-schwa  -4.346817 -4.367245 -4.326389     0
## ae-a      3.459038  3.438610  3.479466     0
## i-a       5.276163  5.255735  5.296591     0
## u-a      -3.264222 -3.284650 -3.243794     0
## i-ae      1.817125  1.796698  1.837553     0
## u-ae     -6.723259 -6.743687 -6.702832     0
## u-i      -8.540385 -8.560813 -8.519957     0
## 
## Call:
## lm(formula = F2 ~ VTRatio + I(VTRatio^2) + vowel + JA + LP + 
##     LD + TCX + TCY + TTX + TTY + TBX + TBY + hyoidX + hyoidY + 
##     (VTRatio:vowel) + (I(VTRatio^2):vowel) + (JA:vowel) + (LP:vowel) + 
##     (LD:vowel) + (TCX:vowel) + (TCY:vowel) + (TTX:vowel) + (TTY:vowel) + 
##     (TBX:vowel) + (TBY:vowel) + (hyoidX:vowel) + (hyoidY:vowel) + 
##     replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.74496 -0.04776 -0.00084  0.04773  1.26351 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           9.830e+00  1.489e+00   6.602 4.81e-11 ***
## VTRatio              -3.992e-01  5.410e+00  -0.074 0.941177    
## I(VTRatio^2)         -3.161e-02  5.457e+00  -0.006 0.995379    
## vowela               -1.263e+00  1.933e+00  -0.653 0.513740    
## vowelae              -1.703e+01  2.088e+00  -8.156 5.08e-16 ***
## voweli               -3.993e+01  1.881e+00 -21.231  < 2e-16 ***
## vowelu                6.479e-01  1.784e+00   0.363 0.716569    
## JA                   -1.143e-03  3.702e-03  -0.309 0.757458    
## LP                    3.706e-03  1.330e-02   0.279 0.780550    
## LD                   -2.460e-03  6.351e-03  -0.387 0.698539    
## TCX                   4.492e-02  2.339e-02   1.921 0.054856 .  
## TCY                  -1.474e-02  1.478e-02  -0.998 0.318432    
## TTX                  -5.801e-03  7.917e-03  -0.733 0.463738    
## TTY                   4.372e-03  7.147e-03   0.612 0.540739    
## TBX                   2.647e-03  3.951e-03   0.670 0.502987    
## TBY                   9.044e-03  6.898e-03   1.311 0.189921    
## hyoidX               -2.023e-02  1.421e-02  -1.423 0.154737    
## hyoidY                3.201e-02  4.211e-02   0.760 0.447267    
## replication           1.267e-04  8.259e-05   1.534 0.125055    
## generation           -6.425e-05  2.795e-05  -2.299 0.021599 *  
## VTRatio:vowela        1.887e+00  7.049e+00   0.268 0.788991    
## VTRatio:vowelae       7.401e+01  7.629e+00   9.701  < 2e-16 ***
## VTRatio:voweli        1.711e+02  7.004e+00  24.428  < 2e-16 ***
## VTRatio:vowelu       -2.343e+01  6.400e+00  -3.661 0.000255 ***
## I(VTRatio^2):vowela  -3.361e+00  7.234e+00  -0.465 0.642299    
## I(VTRatio^2):vowelae -7.399e+01  7.838e+00  -9.441  < 2e-16 ***
## I(VTRatio^2):voweli  -1.693e+02  7.201e+00 -23.506  < 2e-16 ***
## I(VTRatio^2):vowelu   2.826e+01  6.459e+00   4.375 1.26e-05 ***
## vowela:JA            -2.411e-03  6.857e-03  -0.352 0.725186    
## vowelae:JA           -2.438e-03  9.590e-03  -0.254 0.799328    
## voweli:JA            -1.654e-02  5.742e-03  -2.881 0.003992 ** 
## vowelu:JA             1.912e-02  4.678e-03   4.088 4.48e-05 ***
## vowela:LP            -3.017e-02  2.089e-02  -1.444 0.148787    
## vowelae:LP            1.375e-02  2.448e-02   0.562 0.574382    
## voweli:LP             7.469e-03  1.799e-02   0.415 0.678065    
## vowelu:LP            -8.180e-02  1.741e-02  -4.697 2.76e-06 ***
## vowela:LD             1.127e-02  1.009e-02   1.117 0.263962    
## vowelae:LD           -9.698e-03  1.093e-02  -0.887 0.375080    
## voweli:LD             1.411e-02  8.340e-03   1.692 0.090816 .  
## vowelu:LD             4.875e-02  9.780e-03   4.985 6.57e-07 ***
## vowela:TCX            1.497e-01  7.076e-02   2.115 0.034513 *  
## vowelae:TCX          -5.835e-03  3.644e-02  -0.160 0.872813    
## voweli:TCX           -1.531e-01  2.479e-02  -6.176 7.48e-10 ***
## vowelu:TCX            1.607e-01  3.185e-02   5.045 4.81e-07 ***
## vowela:TCY            1.609e-01  4.483e-02   3.590 0.000336 ***
## vowelae:TCY          -5.879e-02  2.955e-02  -1.989 0.046780 *  
## voweli:TCY            1.229e-01  2.520e-02   4.878 1.13e-06 ***
## vowelu:TCY           -2.134e-01  2.383e-02  -8.956  < 2e-16 ***
## vowela:TTX            2.353e-02  1.197e-02   1.966 0.049358 *  
## vowelae:TTX           4.610e-03  1.155e-02   0.399 0.689936    
## voweli:TTX            1.529e-02  9.810e-03   1.559 0.119211    
## vowelu:TTX            2.323e-02  1.114e-02   2.084 0.037230 *  
## vowela:TTY            3.758e-02  1.276e-02   2.946 0.003245 ** 
## vowelae:TTY           1.875e-02  1.795e-02   1.044 0.296446    
## voweli:TTY            2.140e-04  1.076e-02   0.020 0.984125    
## vowelu:TTY           -4.197e-02  9.550e-03  -4.394 1.15e-05 ***
## vowela:TBX            7.386e-04  6.773e-03   0.109 0.913167    
## vowelae:TBX           1.951e-02  1.079e-02   1.809 0.070626 .  
## voweli:TBX           -3.856e-02  1.039e-02  -3.709 0.000212 ***
## vowelu:TBX            7.334e-03  7.815e-03   0.938 0.348097    
## vowela:TBY            4.142e-02  1.164e-02   3.557 0.000380 ***
## vowelae:TBY           1.730e-02  1.995e-02   0.867 0.385863    
## voweli:TBY            2.113e-02  1.982e-02   1.066 0.286559    
## vowelu:TBY            3.316e-02  1.175e-02   2.823 0.004791 ** 
## vowela:hyoidX         1.322e-01  2.841e-02   4.654 3.41e-06 ***
## vowelae:hyoidX        2.515e-03  2.692e-02   0.093 0.925576    
## voweli:hyoidX         1.694e-01  2.357e-02   7.190 8.19e-13 ***
## vowelu:hyoidX         7.940e-02  2.071e-02   3.833 0.000129 ***
## vowela:hyoidY        -1.405e-01  6.125e-02  -2.295 0.021830 *  
## vowelae:hyoidY       -2.251e-01  6.760e-02  -3.330 0.000878 ***
## voweli:hyoidY        -4.368e-01  6.056e-02  -7.213 6.91e-13 ***
## vowelu:hyoidY         9.087e-02  5.793e-02   1.569 0.116839    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1296 on 2928 degrees of freedom
## Multiple R-squared:  0.9981, Adjusted R-squared:  0.9981 
## F-statistic: 2.187e+04 on 71 and 2928 DF,  p-value: < 2.2e-16
##                      Df Sum Sq Mean Sq F value   Pr(>F)    
## VTRatio               1  17.07  17.066 523.315  < 2e-16 ***
## I(VTRatio^2)          1  20.72  20.718 635.290  < 2e-16 ***
## vowel                 4  49.90  12.475 382.524  < 2e-16 ***
## JA                    1   0.00   0.001   0.025 0.875542    
## LP                    1   2.72   2.721  83.447  < 2e-16 ***
## LD                    1   1.62   1.615  49.535 2.42e-12 ***
## TCX                   1   7.59   7.587 232.655  < 2e-16 ***
## TCY                   1   5.71   5.705 174.949  < 2e-16 ***
## TTX                   1   0.93   0.926  28.403 1.06e-07 ***
## TTY                   1   0.93   0.934  28.647 9.35e-08 ***
## TBX                   1   0.04   0.044   1.336 0.247897    
## TBY                   1   0.06   0.061   1.881 0.170274    
## hyoidX                1   5.16   5.161 158.268  < 2e-16 ***
## hyoidY                1   1.65   1.652  50.671 1.37e-12 ***
## replication           1   0.00   0.000   0.014 0.904280    
## generation            1   0.43   0.431  13.201 0.000285 ***
## VTRatio:vowel         4  65.51  16.377 502.195  < 2e-16 ***
## I(VTRatio^2):vowel    4  38.09   9.521 291.963  < 2e-16 ***
## vowel:JA              4   0.71   0.177   5.438 0.000232 ***
## vowel:LP              4   0.25   0.063   1.946 0.100182    
## vowel:LD              4   0.29   0.073   2.247 0.061671 .  
## vowel:TCX             4   3.65   0.912  27.954  < 2e-16 ***
## vowel:TCY             4   4.59   1.147  35.168  < 2e-16 ***
## vowel:TTX             4   0.10   0.024   0.750 0.558167    
## vowel:TTY             4   0.11   0.029   0.877 0.476582    
## vowel:TBX             4   0.36   0.089   2.744 0.027024 *  
## vowel:TBY             4   0.75   0.188   5.755 0.000130 ***
## vowel:hyoidX          4   2.37   0.594  18.202 8.82e-15 ***
## vowel:hyoidY          4   0.22   0.054   1.652 0.158490    
## Residuals          2928  95.49   0.033                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f2e.m0)
## 
## $vowel
##                 diff          lwr         upr     p adj
## a-schwa   0.01425305 -0.014204901  0.04271100 0.6489137
## ae-schwa  0.05080314  0.022345184  0.07926109 0.0000115
## i-schwa   0.35122277  0.322764814  0.37968072 0.0000000
## u-schwa   0.08446132  0.056003367  0.11291927 0.0000000
## ae-a      0.03655009  0.008092134  0.06500804 0.0042182
## i-a       0.33696972  0.308511763  0.36542767 0.0000000
## u-a       0.07020827  0.041750317  0.09866622 0.0000000
## i-ae      0.30041963  0.271961678  0.32887758 0.0000000
## u-ae      0.03365818  0.005200231  0.06211613 0.0110305
## u-i      -0.26676145 -0.295219399 -0.23830349 0.0000000
## 
## Call:
## lm(formula = F2.error ~ VTRatio + I(VTRatio^2) + vowel + JA + 
##     LP + LD + TCX + TCY + TTX + TTY + TBX + TBY + hyoidX + hyoidY + 
##     (VTRatio:vowel) + (I(VTRatio^2):vowel) + (JA:vowel) + (LP:vowel) + 
##     (LD:vowel) + (TCX:vowel) + (TCY:vowel) + (TTX:vowel) + (TTY:vowel) + 
##     (TBX:vowel) + (TBY:vowel) + (hyoidX:vowel) + (hyoidY:vowel) + 
##     replication + generation, data = d)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.5851 -0.0335 -0.0038  0.0225  3.9945 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           1.044e+00  2.074e+00   0.503 0.614707    
## VTRatio              -4.518e+00  7.537e+00  -0.600 0.548864    
## I(VTRatio^2)          5.020e+00  7.602e+00   0.660 0.509059    
## vowela               -4.585e-01  2.693e+00  -0.170 0.864829    
## vowelae               8.376e+00  2.908e+00   2.880 0.004009 ** 
## voweli                6.186e+01  2.620e+00  23.609  < 2e-16 ***
## vowelu                5.147e+00  2.486e+00   2.071 0.038481 *  
## JA                   -3.500e-03  5.157e-03  -0.679 0.497387    
## LP                    4.446e-03  1.853e-02   0.240 0.810377    
## LD                    1.009e-05  8.847e-03   0.001 0.999090    
## TCX                   4.056e-03  3.258e-02   0.124 0.900933    
## TCY                  -2.657e-03  2.058e-02  -0.129 0.897318    
## TTX                  -4.101e-03  1.103e-02  -0.372 0.710059    
## TTY                  -2.424e-03  9.956e-03  -0.243 0.807643    
## TBX                   4.884e-04  5.504e-03   0.089 0.929295    
## TBY                   6.662e-04  9.609e-03   0.069 0.944736    
## hyoidX               -1.840e-02  1.979e-02  -0.930 0.352567    
## hyoidY                1.173e-03  5.867e-02   0.020 0.984044    
## replication          -1.504e-04  1.151e-04  -1.308 0.191075    
## generation           -2.721e-04  3.894e-05  -6.988 3.44e-12 ***
## VTRatio:vowela        2.212e+00  9.820e+00   0.225 0.821758    
## VTRatio:vowelae      -3.199e+01  1.063e+01  -3.010 0.002632 ** 
## VTRatio:voweli       -2.568e+02  9.758e+00 -26.318  < 2e-16 ***
## VTRatio:vowelu       -2.251e+01  8.916e+00  -2.525 0.011631 *  
## I(VTRatio^2):vowela  -2.536e+00  1.008e+01  -0.252 0.801317    
## I(VTRatio^2):vowelae  3.217e+01  1.092e+01   2.947 0.003239 ** 
## I(VTRatio^2):voweli   2.657e+02  1.003e+01  26.491  < 2e-16 ***
## I(VTRatio^2):vowelu   2.592e+01  8.998e+00   2.881 0.003993 ** 
## vowela:JA            -2.266e-03  9.553e-03  -0.237 0.812489    
## vowelae:JA           -1.321e-03  1.336e-02  -0.099 0.921251    
## voweli:JA             2.040e-02  7.999e-03   2.550 0.010810 *  
## vowelu:JA             9.852e-03  6.517e-03   1.512 0.130704    
## vowela:LP            -1.395e-02  2.910e-02  -0.479 0.631701    
## vowelae:LP           -2.143e-02  3.410e-02  -0.628 0.529767    
## voweli:LP            -4.303e-02  2.506e-02  -1.717 0.086121 .  
## vowelu:LP            -7.240e-02  2.426e-02  -2.984 0.002864 ** 
## vowela:LD             3.283e-03  1.406e-02   0.234 0.815324    
## vowelae:LD            8.153e-03  1.523e-02   0.535 0.592464    
## voweli:LD             3.919e-03  1.162e-02   0.337 0.735945    
## vowelu:LD             1.682e-02  1.362e-02   1.235 0.217030    
## vowela:TCX            3.316e-02  9.858e-02   0.336 0.736636    
## vowelae:TCX          -3.338e-02  5.077e-02  -0.658 0.510880    
## voweli:TCX            1.842e-01  3.453e-02   5.334 1.04e-07 ***
## vowelu:TCX            1.546e-01  4.438e-02   3.483 0.000503 ***
## vowela:TCY            2.512e-02  6.246e-02   0.402 0.687598    
## vowelae:TCY           3.074e-02  4.117e-02   0.747 0.455353    
## voweli:TCY            1.547e-01  3.511e-02   4.408 1.08e-05 ***
## vowelu:TCY           -2.541e-01  3.320e-02  -7.652 2.66e-14 ***
## vowela:TTX            2.739e-03  1.667e-02   0.164 0.869520    
## vowelae:TTX          -2.010e-03  1.610e-02  -0.125 0.900606    
## voweli:TTX            3.018e-03  1.367e-02   0.221 0.825223    
## vowelu:TTX           -8.708e-03  1.552e-02  -0.561 0.574908    
## vowela:TTY            1.156e-02  1.777e-02   0.650 0.515489    
## vowelae:TTY          -1.757e-02  2.501e-02  -0.703 0.482293    
## voweli:TTY            1.309e-02  1.498e-02   0.873 0.382542    
## vowelu:TTY           -7.400e-03  1.330e-02  -0.556 0.578106    
## vowela:TBX           -3.451e-04  9.435e-03  -0.037 0.970823    
## vowelae:TBX          -1.125e-02  1.503e-02  -0.748 0.454312    
## voweli:TBX            5.803e-02  1.448e-02   4.007 6.30e-05 ***
## vowelu:TBX            1.733e-02  1.089e-02   1.592 0.111446    
## vowela:TBY            8.136e-03  1.622e-02   0.502 0.615992    
## vowelae:TBY          -1.493e-02  2.779e-02  -0.537 0.591016    
## voweli:TBY            1.211e-01  2.761e-02   4.385 1.20e-05 ***
## vowelu:TBY            3.384e-02  1.637e-02   2.068 0.038737 *  
## vowela:hyoidX         6.197e-03  3.958e-02   0.157 0.875589    
## vowelae:hyoidX       -3.994e-03  3.751e-02  -0.106 0.915200    
## voweli:hyoidX        -2.088e-01  3.283e-02  -6.361 2.31e-10 ***
## vowelu:hyoidX         7.553e-02  2.886e-02   2.618 0.008903 ** 
## vowela:hyoidY        -1.541e-02  8.532e-02  -0.181 0.856638    
## vowelae:hyoidY        1.049e-01  9.417e-02   1.114 0.265354    
## voweli:hyoidY         1.742e-01  8.436e-02   2.065 0.038967 *  
## vowelu:hyoidY         8.771e-02  8.070e-02   1.087 0.277190    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1806 on 2928 degrees of freedom
## Multiple R-squared:  0.708,  Adjusted R-squared:  0.7009 
## F-statistic: 99.99 on 71 and 2928 DF,  p-value: < 2.2e-16

F3

##                      Df Sum Sq Mean Sq  F value   Pr(>F)    
## VTRatio               1  175.1  175.08 2375.113  < 2e-16 ***
## I(VTRatio^2)          1   94.4   94.37 1280.151  < 2e-16 ***
## vowel                 4  407.0  101.75 1380.313  < 2e-16 ***
## JA                    1    0.4    0.41    5.499 0.019096 *  
## LP                    1    0.1    0.15    1.973 0.160205    
## LD                    1    0.5    0.46    6.192 0.012892 *  
## TCX                   1   20.3   20.31  275.553  < 2e-16 ***
## TCY                   1    0.4    0.42    5.663 0.017386 *  
## TTX                   1    0.2    0.24    3.218 0.072916 .  
## TTY                   1    0.4    0.35    4.791 0.028680 *  
## TBX                   1    4.3    4.32   58.542 2.68e-14 ***
## TBY                   1    0.0    0.00    0.036 0.850276    
## hyoidX                1    0.3    0.28    3.842 0.050079 .  
## hyoidY                1   16.0   16.00  217.061  < 2e-16 ***
## replication           1    0.0    0.02    0.310 0.577679    
## generation            1    1.0    1.02   13.814 0.000206 ***
## VTRatio:vowel         4   13.2    3.29   44.668  < 2e-16 ***
## I(VTRatio^2):vowel    4   29.6    7.40  100.346  < 2e-16 ***
## vowel:JA              4    2.7    0.68    9.213 2.14e-07 ***
## vowel:LP              4    1.0    0.25    3.436 0.008261 ** 
## vowel:LD              4    1.6    0.40    5.438 0.000232 ***
## vowel:TCX             4    1.7    0.43    5.775 0.000126 ***
## vowel:TCY             4   22.3    5.57   75.497  < 2e-16 ***
## vowel:TTX             4    0.1    0.03    0.459 0.765996    
## vowel:TTY             4    2.7    0.67    9.081 2.74e-07 ***
## vowel:TBX             4    0.4    0.09    1.237 0.292984    
## vowel:TBY             4    1.7    0.44    5.929 9.48e-05 ***
## vowel:hyoidX          4    3.0    0.74   10.101 4.05e-08 ***
## vowel:hyoidY          4   10.5    2.64   35.767  < 2e-16 ***
## Residuals          2928  215.8    0.07                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f3.m0)
## 
## $vowel
##                diff         lwr        upr p adj
## a-schwa   0.3696720  0.32688632  0.4124578     0
## ae-schwa  0.1057591  0.06297336  0.1485448     0
## i-schwa   1.0513291  1.00854338  1.0941148     0
## u-schwa   0.4783480  0.43556226  0.5211337     0
## ae-a     -0.2639130 -0.30669869 -0.2211272     0
## i-a       0.6816571  0.63887134  0.7244428     0
## u-a       0.1086759  0.06589021  0.1514617     0
## i-ae      0.9455700  0.90278430  0.9883557     0
## u-ae      0.3725889  0.32980317  0.4153746     0
## u-i      -0.5729811 -0.61576685 -0.5301954     0
## 
## Call:
## lm(formula = F3 ~ VTRatio + I(VTRatio^2) + vowel + JA + LP + 
##     LD + TCX + TCY + TTX + TTY + TBX + TBY + hyoidX + hyoidY + 
##     (VTRatio:vowel) + (I(VTRatio^2):vowel) + (JA:vowel) + (LP:vowel) + 
##     (LD:vowel) + (TCX:vowel) + (TCY:vowel) + (TTX:vowel) + (TTY:vowel) + 
##     (TBX:vowel) + (TBY:vowel) + (hyoidX:vowel) + (hyoidY:vowel) + 
##     replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.54411 -0.11100 -0.00309  0.09924  1.60499 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          -2.179e+01  3.119e+00  -6.986 3.50e-12 ***
## VTRatio               1.485e+02  1.133e+01  13.106  < 2e-16 ***
## I(VTRatio^2)         -1.542e+02  1.143e+01 -13.496  < 2e-16 ***
## vowela               -2.085e+01  4.049e+00  -5.149 2.79e-07 ***
## vowelae               2.766e-01  4.373e+00   0.063 0.949573    
## voweli               -6.113e+00  3.939e+00  -1.552 0.120773    
## vowelu                4.957e+00  3.738e+00   1.326 0.184818    
## JA                   -2.299e-03  7.753e-03  -0.297 0.766813    
## LP                   -1.988e-02  2.785e-02  -0.714 0.475459    
## LD                    8.422e-03  1.330e-02   0.633 0.526642    
## TCX                  -2.232e-01  4.898e-02  -4.556 5.42e-06 ***
## TCY                  -6.433e-02  3.095e-02  -2.079 0.037746 *  
## TTX                   1.559e-02  1.658e-02   0.940 0.347112    
## TTY                   1.185e-02  1.497e-02   0.792 0.428469    
## TBX                   2.954e-02  8.275e-03   3.570 0.000363 ***
## TBY                   2.621e-02  1.445e-02   1.814 0.069809 .  
## hyoidX               -3.724e-02  2.976e-02  -1.251 0.210953    
## hyoidY               -1.102e-01  8.821e-02  -1.249 0.211663    
## replication           7.241e-05  1.730e-04   0.419 0.675519    
## generation           -8.469e-05  5.855e-05  -1.447 0.148133    
## VTRatio:vowela        6.778e+01  1.476e+01   4.591 4.60e-06 ***
## VTRatio:vowelae      -2.685e-01  1.598e+01  -0.017 0.986592    
## VTRatio:voweli        2.176e+01  1.467e+01   1.483 0.138146    
## VTRatio:vowelu       -5.831e+01  1.341e+01  -4.350 1.41e-05 ***
## I(VTRatio^2):vowela  -5.906e+01  1.515e+01  -3.898 9.92e-05 ***
## I(VTRatio^2):vowelae  2.333e-01  1.642e+01   0.014 0.988660    
## I(VTRatio^2):voweli  -2.024e+01  1.508e+01  -1.342 0.179713    
## I(VTRatio^2):vowelu   8.146e+01  1.353e+01   6.021 1.94e-09 ***
## vowela:JA             8.435e-03  1.436e-02   0.587 0.557015    
## vowelae:JA            1.934e-02  2.009e-02   0.963 0.335651    
## voweli:JA            -3.224e-02  1.203e-02  -2.680 0.007396 ** 
## vowelu:JA            -1.912e-02  9.798e-03  -1.951 0.051146 .  
## vowela:LP            -3.733e-03  4.376e-02  -0.085 0.932020    
## vowelae:LP            8.523e-02  5.127e-02   1.662 0.096543 .  
## voweli:LP             4.233e-02  3.768e-02   1.123 0.261404    
## vowelu:LP             9.903e-02  3.647e-02   2.715 0.006662 ** 
## vowela:LD            -1.275e-02  2.113e-02  -0.603 0.546480    
## vowelae:LD           -2.364e-02  2.290e-02  -1.032 0.301987    
## voweli:LD             1.488e-03  1.747e-02   0.085 0.932129    
## vowelu:LD            -6.237e-02  2.048e-02  -3.045 0.002349 ** 
## vowela:TCX           -9.042e-01  1.482e-01  -6.101 1.19e-09 ***
## vowelae:TCX          -1.565e-02  7.633e-02  -0.205 0.837550    
## voweli:TCX            7.645e-02  5.192e-02   1.473 0.140990    
## vowelu:TCX           -3.307e-01  6.672e-02  -4.957 7.58e-07 ***
## vowela:TCY           -5.402e-01  9.390e-02  -5.753 9.70e-09 ***
## vowelae:TCY          -1.009e-01  6.190e-02  -1.630 0.103303    
## voweli:TCY           -2.144e-01  5.278e-02  -4.061 5.01e-05 ***
## vowelu:TCY            4.948e-01  4.991e-02   9.912  < 2e-16 ***
## vowela:TTX            1.850e-02  2.507e-02   0.738 0.460685    
## vowelae:TTX          -2.327e-02  2.420e-02  -0.962 0.336357    
## voweli:TTX           -1.223e-02  2.055e-02  -0.595 0.551703    
## vowelu:TTX           -2.249e-02  2.334e-02  -0.964 0.335287    
## vowela:TTY           -1.303e-01  2.672e-02  -4.876 1.14e-06 ***
## vowelae:TTY          -6.985e-02  3.760e-02  -1.858 0.063307 .  
## voweli:TTY           -1.698e-02  2.253e-02  -0.754 0.451052    
## vowelu:TTY            4.401e-02  2.000e-02   2.200 0.027888 *  
## vowela:TBX           -1.836e-02  1.419e-02  -1.294 0.195660    
## vowelae:TBX          -3.893e-02  2.259e-02  -1.723 0.084994 .  
## voweli:TBX           -3.004e-02  2.177e-02  -1.380 0.167695    
## vowelu:TBX            3.125e-02  1.637e-02   1.909 0.056303 .  
## vowela:TBY           -8.925e-02  2.439e-02  -3.660 0.000257 ***
## vowelae:TBY          -1.682e-01  4.178e-02  -4.027 5.80e-05 ***
## voweli:TBY           -1.599e-01  4.152e-02  -3.851 0.000120 ***
## vowelu:TBY           -3.248e-02  2.461e-02  -1.320 0.186975    
## vowela:hyoidX        -2.938e-01  5.951e-02  -4.937 8.37e-07 ***
## vowelae:hyoidX       -1.133e-01  5.639e-02  -2.009 0.044620 *  
## voweli:hyoidX         1.184e-01  4.936e-02   2.400 0.016474 *  
## vowelu:hyoidX        -2.760e-02  4.338e-02  -0.636 0.524753    
## vowela:hyoidY        -5.501e-02  1.283e-01  -0.429 0.668071    
## vowelae:hyoidY       -1.664e-02  1.416e-01  -0.118 0.906454    
## voweli:hyoidY        -4.235e-01  1.268e-01  -3.339 0.000851 ***
## vowelu:hyoidY        -1.219e+00  1.213e-01 -10.050  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2715 on 2928 degrees of freedom
## Multiple R-squared:  0.7898, Adjusted R-squared:  0.7847 
## F-statistic: 154.9 on 71 and 2928 DF,  p-value: < 2.2e-16
##                      Df Sum Sq Mean Sq  F value   Pr(>F)    
## VTRatio               1  316.6   316.6 2686.638  < 2e-16 ***
## I(VTRatio^2)          1  215.3   215.3 1827.398  < 2e-16 ***
## vowel                 4   64.4    16.1  136.621  < 2e-16 ***
## JA                    1   12.8    12.8  108.808  < 2e-16 ***
## LP                    1    0.2     0.2    1.353 0.244866    
## LD                    1    2.2     2.2   18.688 1.59e-05 ***
## TCX                   1   39.5    39.5  334.969  < 2e-16 ***
## TCY                   1    0.2     0.2    1.424 0.232868    
## TTX                   1    3.0     3.0   25.382 4.99e-07 ***
## TTY                   1   14.7    14.7  124.838  < 2e-16 ***
## TBX                   1    8.6     8.6   73.406  < 2e-16 ***
## TBY                   1    3.7     3.7   31.637 2.03e-08 ***
## hyoidX                1    0.0     0.0    0.214 0.643713    
## hyoidY                1    1.0     1.0    8.451 0.003675 ** 
## replication           1    0.0     0.0    0.059 0.808846    
## generation            1    1.7     1.7   14.202 0.000167 ***
## VTRatio:vowel         4   76.2    19.0  161.608  < 2e-16 ***
## I(VTRatio^2):vowel    4   27.7     6.9   58.786  < 2e-16 ***
## vowel:JA              4    4.0     1.0    8.485 8.36e-07 ***
## vowel:LP              4    4.3     1.1    9.229 2.08e-07 ***
## vowel:LD              4    3.3     0.8    7.088 1.12e-05 ***
## vowel:TCX             4    7.9     2.0   16.762 1.36e-13 ***
## vowel:TCY             4   20.3     5.1   42.984  < 2e-16 ***
## vowel:TTX             4    1.3     0.3    2.773 0.025739 *  
## vowel:TTY             4   17.8     4.5   37.841  < 2e-16 ***
## vowel:TBX             4    0.9     0.2    2.002 0.091556 .  
## vowel:TBY             4    1.3     0.3    2.730 0.027659 *  
## vowel:hyoidX          4    4.8     1.2   10.245 3.09e-08 ***
## vowel:hyoidY          4    4.6     1.1    9.659 9.28e-08 ***
## Residuals          2928  345.0     0.1                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f3e.m0)
## 
## $vowel
##                  diff         lwr         upr     p adj
## a-schwa   0.261057929  0.20696287  0.31515299 0.0000000
## ae-schwa  0.073818843  0.01972379  0.12791390 0.0018619
## i-schwa  -0.009728477 -0.06382354  0.04436658 0.9882271
## u-schwa   0.355169026  0.30107397  0.40926408 0.0000000
## ae-a     -0.187239086 -0.24133414 -0.13314403 0.0000000
## i-a      -0.270786406 -0.32488146 -0.21669135 0.0000000
## u-a       0.094111097  0.04001604  0.14820616 0.0000212
## i-ae     -0.083547321 -0.13764238 -0.02945226 0.0002484
## u-ae      0.281350183  0.22725512  0.33544524 0.0000000
## u-i       0.364897504  0.31080245  0.41899256 0.0000000
## 
## Call:
## lm(formula = F3.error ~ VTRatio + I(VTRatio^2) + vowel + JA + 
##     LP + LD + TCX + TCY + TTX + TTY + TBX + TBY + hyoidX + hyoidY + 
##     (VTRatio:vowel) + (I(VTRatio^2):vowel) + (JA:vowel) + (LP:vowel) + 
##     (LD:vowel) + (TCX:vowel) + (TCY:vowel) + (TTX:vowel) + (TTY:vowel) + 
##     (TBX:vowel) + (TBY:vowel) + (hyoidX:vowel) + (hyoidY:vowel) + 
##     replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.76486 -0.12280 -0.00143  0.11852  2.46934 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           3.266e+01  3.943e+00   8.284  < 2e-16 ***
## VTRatio              -1.406e+02  1.433e+01  -9.816  < 2e-16 ***
## I(VTRatio^2)          1.494e+02  1.445e+01  10.337  < 2e-16 ***
## vowela                4.957e+01  5.120e+00   9.682  < 2e-16 ***
## vowelae               2.314e+00  5.529e+00   0.419 0.675561    
## voweli                2.458e+00  4.980e+00   0.493 0.621711    
## vowelu                2.151e+01  4.725e+00   4.552 5.52e-06 ***
## JA                    6.457e-03  9.802e-03   0.659 0.510129    
## LP                    1.726e-02  3.522e-02   0.490 0.624134    
## LD                   -5.772e-03  1.682e-02  -0.343 0.731458    
## TCX                   2.360e-01  6.193e-02   3.811 0.000141 ***
## TCY                   1.023e-01  3.913e-02   2.614 0.009004 ** 
## TTX                  -7.663e-04  2.096e-02  -0.037 0.970844    
## TTY                  -6.599e-03  1.893e-02  -0.349 0.727362    
## TBX                  -2.816e-02  1.046e-02  -2.692 0.007147 ** 
## TBY                  -3.217e-02  1.827e-02  -1.761 0.078276 .  
## hyoidX                8.252e-02  3.763e-02   2.193 0.028388 *  
## hyoidY               -1.490e-01  1.115e-01  -1.336 0.181623    
## replication          -3.934e-05  2.187e-04  -0.180 0.857265    
## generation           -4.947e-05  7.402e-05  -0.668 0.503995    
## VTRatio:vowela       -1.712e+02  1.867e+01  -9.170  < 2e-16 ***
## VTRatio:vowelae       1.652e+00  2.020e+01   0.082 0.934837    
## VTRatio:voweli       -6.445e+00  1.855e+01  -0.347 0.728250    
## VTRatio:vowelu       -6.843e+01  1.695e+01  -4.037 5.54e-05 ***
## I(VTRatio^2):vowela   1.587e+02  1.916e+01   8.283  < 2e-16 ***
## I(VTRatio^2):vowelae -6.770e+00  2.075e+01  -0.326 0.744309    
## I(VTRatio^2):voweli   4.877e+00  1.907e+01   0.256 0.798149    
## I(VTRatio^2):vowelu   6.079e+01  1.710e+01   3.554 0.000385 ***
## vowela:JA             6.159e-03  1.816e-02   0.339 0.734491    
## vowelae:JA            1.585e-02  2.540e-02   0.624 0.532647    
## voweli:JA             2.303e-02  1.521e-02   1.514 0.130052    
## vowelu:JA             3.250e-02  1.239e-02   2.623 0.008755 ** 
## vowela:LP            -1.727e-02  5.532e-02  -0.312 0.754938    
## vowelae:LP           -3.574e-02  6.482e-02  -0.551 0.581445    
## voweli:LP            -7.998e-02  4.764e-02  -1.679 0.093321 .  
## vowelu:LP            -2.386e-01  4.611e-02  -5.174 2.45e-07 ***
## vowela:LD             3.773e-02  2.672e-02   1.412 0.158040    
## vowelae:LD            2.279e-02  2.895e-02   0.787 0.431256    
## voweli:LD             9.309e-03  2.209e-02   0.421 0.673440    
## vowelu:LD             9.655e-02  2.590e-02   3.728 0.000196 ***
## vowela:TCX            2.492e+00  1.874e-01  13.299  < 2e-16 ***
## vowelae:TCX          -1.974e-01  9.651e-02  -2.046 0.040852 *  
## voweli:TCX           -4.775e-02  6.564e-02  -0.727 0.467016    
## vowelu:TCX            3.832e-01  8.435e-02   4.543 5.77e-06 ***
## vowela:TCY            1.318e+00  1.187e-01  11.099  < 2e-16 ***
## vowelae:TCY           1.165e-02  7.826e-02   0.149 0.881657    
## voweli:TCY            9.497e-02  6.673e-02   1.423 0.154787    
## vowelu:TCY           -2.421e-01  6.311e-02  -3.837 0.000127 ***
## vowela:TTX           -7.080e-02  3.169e-02  -2.234 0.025559 *  
## vowelae:TTX          -3.451e-02  3.060e-02  -1.128 0.259398    
## voweli:TTX            2.277e-03  2.598e-02   0.088 0.930165    
## vowelu:TTX            6.823e-02  2.951e-02   2.312 0.020842 *  
## vowela:TTY            2.095e-01  3.378e-02   6.202 6.36e-10 ***
## vowelae:TTY           1.447e-02  4.754e-02   0.304 0.760799    
## voweli:TTY            1.638e-03  2.848e-02   0.057 0.954151    
## vowelu:TTY           -1.918e-01  2.529e-02  -7.585 4.44e-14 ***
## vowela:TBX            5.835e-03  1.794e-02   0.325 0.744940    
## vowelae:TBX           1.225e-02  2.856e-02   0.429 0.668161    
## voweli:TBX            3.495e-02  2.752e-02   1.270 0.204228    
## vowelu:TBX           -5.482e-02  2.070e-02  -2.649 0.008121 ** 
## vowela:TBY            5.099e-02  3.083e-02   1.654 0.098282 .  
## vowelae:TBY           4.703e-02  5.282e-02   0.890 0.373372    
## voweli:TBY            1.531e-01  5.249e-02   2.917 0.003558 ** 
## vowelu:TBY           -6.498e-03  3.111e-02  -0.209 0.834562    
## vowela:hyoidX         3.923e-01  7.523e-02   5.214 1.97e-07 ***
## vowelae:hyoidX        2.903e-02  7.130e-02   0.407 0.683904    
## voweli:hyoidX        -1.800e-01  6.240e-02  -2.885 0.003949 ** 
## vowelu:hyoidX         5.923e-03  5.485e-02   0.108 0.914022    
## vowela:hyoidY        -2.529e-01  1.622e-01  -1.559 0.119032    
## vowelae:hyoidY        3.215e-01  1.790e-01   1.796 0.072538 .  
## voweli:hyoidY         2.921e-01  1.604e-01   1.821 0.068651 .  
## vowelu:hyoidY         6.628e-01  1.534e-01   4.321 1.61e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3433 on 2928 degrees of freedom
## Multiple R-squared:  0.7133, Adjusted R-squared:  0.7063 
## F-statistic: 102.6 on 71 and 2928 DF,  p-value: < 2.2e-16

F4

##                      Df Sum Sq Mean Sq  F value   Pr(>F)    
## VTRatio               1  57.27   57.27 1143.502  < 2e-16 ***
## I(VTRatio^2)          1   0.80    0.80   15.881 6.91e-05 ***
## vowel                 4 165.33   41.33  825.253  < 2e-16 ***
## JA                    1   0.18    0.18    3.655 0.056009 .  
## LP                    1   1.69    1.69   33.699 7.12e-09 ***
## LD                    1   0.61    0.61   12.170 0.000493 ***
## TCX                   1   4.25    4.25   84.955  < 2e-16 ***
## TCY                   1   0.04    0.04    0.722 0.395422    
## TTX                   1   1.94    1.94   38.774 5.44e-10 ***
## TTY                   1  17.62   17.62  351.914  < 2e-16 ***
## TBX                   1   0.46    0.46    9.269 0.002351 ** 
## TBY                   1   0.54    0.54   10.870 0.000989 ***
## hyoidX                1   0.07    0.07    1.385 0.239395    
## hyoidY                1  13.55   13.55  270.575  < 2e-16 ***
## replication           1   0.04    0.04    0.816 0.366486    
## generation            1   2.67    2.67   53.270 3.73e-13 ***
## VTRatio:vowel         4  10.25    2.56   51.162  < 2e-16 ***
## I(VTRatio^2):vowel    4  19.42    4.85   96.914  < 2e-16 ***
## vowel:JA              4   2.45    0.61   12.221 7.44e-10 ***
## vowel:LP              4   2.48    0.62   12.390 5.41e-10 ***
## vowel:LD              4   0.82    0.20    4.086 0.002635 ** 
## vowel:TCX             4  11.06    2.77   55.228  < 2e-16 ***
## vowel:TCY             4   9.20    2.30   45.917  < 2e-16 ***
## vowel:TTX             4   0.86    0.22    4.300 0.001802 ** 
## vowel:TTY             4   2.14    0.53   10.670 1.39e-08 ***
## vowel:TBX             4   0.06    0.01    0.285 0.887820    
## vowel:TBY             4   0.34    0.08    1.688 0.149898    
## vowel:hyoidX          4   9.41    2.35   46.986  < 2e-16 ***
## vowel:hyoidY          4   5.75    1.44   28.715  < 2e-16 ***
## Residuals          2928 146.64    0.05                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f4.m0)
## 
## $vowel
##                 diff         lwr          upr     p adj
## a-schwa  -0.18780768 -0.22307437 -0.152540987 0.0000000
## ae-schwa  0.02453996 -0.01072673  0.059806653 0.3178526
## i-schwa   0.50724987  0.47198318  0.542516559 0.0000000
## u-schwa  -0.03593817 -0.07120486 -0.000671475 0.0432930
## ae-a      0.21234764  0.17708095  0.247614331 0.0000000
## i-a       0.69505755  0.65979085  0.730324237 0.0000000
## u-a       0.15186951  0.11660282  0.187136203 0.0000000
## i-ae      0.48270991  0.44744322  0.517976598 0.0000000
## u-ae     -0.06047813 -0.09574482 -0.025211436 0.0000294
## u-i      -0.54318803 -0.57845473 -0.507921343 0.0000000
## 
## Call:
## lm(formula = F4 ~ VTRatio + I(VTRatio^2) + vowel + JA + LP + 
##     LD + TCX + TCY + TTX + TTY + TBX + TBY + hyoidX + hyoidY + 
##     (VTRatio:vowel) + (I(VTRatio^2):vowel) + (JA:vowel) + (LP:vowel) + 
##     (LD:vowel) + (TCX:vowel) + (TCY:vowel) + (TTX:vowel) + (TTY:vowel) + 
##     (TBX:vowel) + (TBY:vowel) + (hyoidX:vowel) + (hyoidY:vowel) + 
##     replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.00045 -0.09732 -0.00753  0.08541  1.67701 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          -9.029e-01  2.571e+00  -0.351 0.725441    
## VTRatio               6.137e+01  9.340e+00   6.571 5.91e-11 ***
## I(VTRatio^2)         -6.053e+01  9.421e+00  -6.426 1.53e-10 ***
## vowela               -1.336e+01  3.338e+00  -4.003 6.42e-05 ***
## vowelae              -1.329e+00  3.604e+00  -0.369 0.712271    
## voweli                1.123e+01  3.247e+00   3.459 0.000551 ***
## vowelu                2.121e+01  3.081e+00   6.886 7.01e-12 ***
## JA                    4.581e-03  6.390e-03   0.717 0.473541    
## LP                    2.974e-02  2.296e-02   1.295 0.195271    
## LD                   -1.829e-02  1.096e-02  -1.668 0.095401 .  
## TCX                   1.057e-01  4.037e-02   2.619 0.008874 ** 
## TCY                  -7.770e-02  2.551e-02  -3.046 0.002338 ** 
## TTX                  -5.119e-02  1.367e-02  -3.745 0.000184 ***
## TTY                  -1.970e-02  1.234e-02  -1.597 0.110448    
## TBX                   1.828e-02  6.821e-03   2.679 0.007415 ** 
## TBY                   4.203e-02  1.191e-02   3.530 0.000422 ***
## hyoidX                2.719e-02  2.453e-02   1.108 0.267779    
## hyoidY               -3.965e-01  7.270e-02  -5.454 5.33e-08 ***
## replication           2.677e-05  1.426e-04   0.188 0.851074    
## generation           -6.110e-05  4.826e-05  -1.266 0.205596    
## VTRatio:vowela        5.204e+01  1.217e+01   4.276 1.96e-05 ***
## VTRatio:vowelae       3.867e+00  1.317e+01   0.294 0.769083    
## VTRatio:voweli       -4.305e+01  1.209e+01  -3.560 0.000377 ***
## VTRatio:vowelu       -1.047e+02  1.105e+01  -9.476  < 2e-16 ***
## I(VTRatio^2):vowela  -5.469e+01  1.249e+01  -4.379 1.23e-05 ***
## I(VTRatio^2):vowelae -2.113e-01  1.353e+01  -0.016 0.987543    
## I(VTRatio^2):voweli   4.515e+01  1.243e+01   3.632 0.000286 ***
## I(VTRatio^2):vowelu   1.224e+02  1.115e+01  10.975  < 2e-16 ***
## vowela:JA             1.458e-03  1.184e-02   0.123 0.901962    
## vowelae:JA           -1.755e-02  1.656e-02  -1.060 0.289282    
## voweli:JA            -3.957e-02  9.913e-03  -3.991 6.73e-05 ***
## vowelu:JA            -2.589e-03  8.076e-03  -0.321 0.748592    
## vowela:LP            -1.164e-02  3.607e-02  -0.323 0.746932    
## vowelae:LP           -5.536e-02  4.226e-02  -1.310 0.190281    
## voweli:LP            -4.144e-02  3.106e-02  -1.334 0.182299    
## vowelu:LP            -1.582e-01  3.006e-02  -5.263 1.52e-07 ***
## vowela:LD             2.966e-02  1.742e-02   1.703 0.088730 .  
## vowelae:LD            2.151e-02  1.887e-02   1.140 0.254461    
## voweli:LD             6.254e-02  1.440e-02   4.344 1.45e-05 ***
## vowelu:LD             2.618e-02  1.688e-02   1.551 0.121042    
## vowela:TCX            9.317e-01  1.222e-01   7.627 3.23e-14 ***
## vowelae:TCX          -6.411e-02  6.292e-02  -1.019 0.308275    
## voweli:TCX           -1.229e-01  4.279e-02  -2.873 0.004096 ** 
## vowelu:TCX           -5.532e-01  5.499e-02 -10.060  < 2e-16 ***
## vowela:TCY            7.150e-01  7.740e-02   9.238  < 2e-16 ***
## vowelae:TCY           7.622e-02  5.102e-02   1.494 0.135297    
## voweli:TCY            4.483e-02  4.350e-02   1.030 0.302899    
## vowelu:TCY            4.823e-01  4.114e-02  11.723  < 2e-16 ***
## vowela:TTX            5.206e-02  2.066e-02   2.519 0.011807 *  
## vowelae:TTX           4.153e-02  1.995e-02   2.082 0.037436 *  
## voweli:TTX            4.224e-02  1.694e-02   2.494 0.012689 *  
## vowelu:TTX            2.810e-02  1.924e-02   1.461 0.144239    
## vowela:TTY            7.180e-02  2.203e-02   3.260 0.001127 ** 
## vowelae:TTY           5.709e-02  3.099e-02   1.842 0.065566 .  
## voweli:TTY           -8.636e-03  1.857e-02  -0.465 0.641896    
## vowelu:TTY           -8.914e-02  1.649e-02  -5.407 6.94e-08 ***
## vowela:TBX            2.669e-02  1.169e-02   2.283 0.022512 *  
## vowelae:TBX          -4.573e-03  1.862e-02  -0.246 0.806052    
## voweli:TBX            1.651e-03  1.794e-02   0.092 0.926689    
## vowelu:TBX           -8.421e-03  1.349e-02  -0.624 0.532567    
## vowela:TBY            4.327e-02  2.010e-02   2.152 0.031440 *  
## vowelae:TBY          -3.375e-02  3.444e-02  -0.980 0.327195    
## voweli:TBY           -9.226e-03  3.422e-02  -0.270 0.787494    
## vowelu:TBY           -4.560e-02  2.028e-02  -2.248 0.024628 *  
## vowela:hyoidX         4.786e-01  4.905e-02   9.757  < 2e-16 ***
## vowelae:hyoidX        9.779e-02  4.648e-02   2.104 0.035485 *  
## voweli:hyoidX        -3.366e-01  4.068e-02  -8.274  < 2e-16 ***
## vowelu:hyoidX        -8.931e-02  3.576e-02  -2.497 0.012563 *  
## vowela:hyoidY        -8.182e-01  1.057e-01  -7.738 1.38e-14 ***
## vowelae:hyoidY        8.190e-02  1.167e-01   0.702 0.482827    
## voweli:hyoidY         2.362e-01  1.045e-01   2.259 0.023962 *  
## vowelu:hyoidY        -2.491e-01  1.000e-01  -2.491 0.012805 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2238 on 2928 degrees of freedom
## Multiple R-squared:  0.6995, Adjusted R-squared:  0.6922 
## F-statistic: 95.98 on 71 and 2928 DF,  p-value: < 2.2e-16
##                      Df Sum Sq Mean Sq F value   Pr(>F)    
## VTRatio               1   0.14   0.141   1.986 0.158904    
## I(VTRatio^2)          1   3.50   3.504  49.177 2.89e-12 ***
## vowel                 4  23.83   5.958  83.631  < 2e-16 ***
## JA                    1   0.57   0.570   7.994 0.004725 ** 
## LP                    1   1.76   1.764  24.754 6.89e-07 ***
## LD                    1   0.05   0.046   0.651 0.419974    
## TCX                   1   5.83   5.833  81.873  < 2e-16 ***
## TCY                   1   0.81   0.813  11.412 0.000739 ***
## TTX                   1   0.02   0.021   0.301 0.583541    
## TTY                   1  26.14  26.145 366.966  < 2e-16 ***
## TBX                   1   1.47   1.475  20.699 5.59e-06 ***
## TBY                   1   0.14   0.135   1.900 0.168196    
## hyoidX                1   2.14   2.135  29.973 4.75e-08 ***
## hyoidY                1   0.01   0.007   0.103 0.747705    
## replication           1   0.00   0.003   0.043 0.836177    
## generation            1   6.50   6.503  91.280  < 2e-16 ***
## VTRatio:vowel         4  11.60   2.900  40.699  < 2e-16 ***
## I(VTRatio^2):vowel    4  11.78   2.945  41.339  < 2e-16 ***
## vowel:JA              4   1.69   0.422   5.921 9.62e-05 ***
## vowel:LP              4   2.67   0.668   9.375 1.58e-07 ***
## vowel:LD              4   0.43   0.107   1.503 0.198434    
## vowel:TCX             4   7.53   1.883  26.424  < 2e-16 ***
## vowel:TCY             4   1.75   0.438   6.146 6.37e-05 ***
## vowel:TTX             4   0.27   0.069   0.964 0.425915    
## vowel:TTY             4   6.35   1.588  22.284  < 2e-16 ***
## vowel:TBX             4   0.46   0.115   1.608 0.169458    
## vowel:TBY             4   1.77   0.443   6.222 5.54e-05 ***
## vowel:hyoidX          4   3.48   0.871  12.228 7.34e-10 ***
## vowel:hyoidY          4   1.26   0.314   4.406 0.001492 ** 
## Residuals          2928 208.61   0.071                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f4e.m0)
## 
## $vowel
##                 diff         lwr         upr     p adj
## a-schwa   0.07730482  0.03524198 0.119367651 0.0000055
## ae-schwa  0.09414493  0.05208210 0.136207763 0.0000000
## i-schwa   0.05435520  0.01229236 0.096418029 0.0039014
## u-schwa   0.26453127  0.22246844 0.306594107 0.0000000
## ae-a      0.01684011 -0.02522272 0.058902945 0.8103709
## i-a      -0.02294962 -0.06501245 0.019113212 0.5695922
## u-a       0.18722646  0.14516362 0.229289290 0.0000000
## i-ae     -0.03978973 -0.08185257 0.002273099 0.0739411
## u-ae      0.17038634  0.12832351 0.212449178 0.0000000
## u-i       0.21017608  0.16811324 0.252238911 0.0000000
## 
## Call:
## lm(formula = F4.error ~ VTRatio + I(VTRatio^2) + vowel + JA + 
##     LP + LD + TCX + TCY + TTX + TTY + TBX + TBY + hyoidX + hyoidY + 
##     (VTRatio:vowel) + (I(VTRatio^2):vowel) + (JA:vowel) + (LP:vowel) + 
##     (LD:vowel) + (TCX:vowel) + (TCY:vowel) + (TTX:vowel) + (TTY:vowel) + 
##     (TBX:vowel) + (TBY:vowel) + (hyoidX:vowel) + (hyoidY:vowel) + 
##     replication + generation, data = d)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.0931 -0.0522 -0.0111  0.0382  4.3396 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           1.741e+00  3.066e+00   0.568 0.570161    
## VTRatio              -9.289e+00  1.114e+01  -0.834 0.404410    
## I(VTRatio^2)          1.090e+01  1.124e+01   0.970 0.332041    
## vowela               -1.359e+00  3.981e+00  -0.341 0.732811    
## vowelae               8.982e+00  4.299e+00   2.089 0.036772 *  
## voweli               -5.318e+00  3.873e+00  -1.373 0.169805    
## vowelu                8.069e+00  3.674e+00   2.196 0.028164 *  
## JA                    1.658e-03  7.622e-03   0.218 0.827804    
## LP                    9.493e-03  2.738e-02   0.347 0.728874    
## LD                    4.526e-04  1.308e-02   0.035 0.972391    
## TCX                   7.757e-02  4.815e-02   1.611 0.107304    
## TCY                  -1.273e-02  3.042e-02  -0.418 0.675629    
## TTX                   1.284e-02  1.630e-02   0.788 0.430883    
## TTY                  -2.040e-02  1.472e-02  -1.386 0.165766    
## TBX                  -1.759e-02  8.135e-03  -2.162 0.030708 *  
## TBY                  -8.583e-03  1.420e-02  -0.604 0.545680    
## hyoidX               -5.270e-03  2.926e-02  -0.180 0.857079    
## hyoidY               -5.738e-02  8.671e-02  -0.662 0.508216    
## replication          -7.574e-05  1.701e-04  -0.445 0.656085    
## generation           -3.189e-04  5.756e-05  -5.540 3.29e-08 ***
## VTRatio:vowela        9.270e+00  1.451e+01   0.639 0.523058    
## VTRatio:vowelae      -3.497e+01  1.571e+01  -2.226 0.026083 *  
## VTRatio:voweli        1.542e+01  1.442e+01   1.069 0.285022    
## VTRatio:vowelu       -5.354e+01  1.318e+01  -4.063 4.98e-05 ***
## I(VTRatio^2):vowela  -1.179e+01  1.490e+01  -0.792 0.428597    
## I(VTRatio^2):vowelae  3.453e+01  1.614e+01   2.139 0.032487 *  
## I(VTRatio^2):voweli  -1.351e+01  1.483e+01  -0.911 0.362450    
## I(VTRatio^2):vowelu   7.148e+01  1.330e+01   5.375 8.28e-08 ***
## vowela:JA            -2.826e-03  1.412e-02  -0.200 0.841356    
## vowelae:JA           -7.421e-03  1.975e-02  -0.376 0.707086    
## voweli:JA            -1.869e-02  1.182e-02  -1.581 0.113997    
## vowelu:JA             9.193e-03  9.633e-03   0.954 0.340000    
## vowela:LP            -3.360e-03  4.302e-02  -0.078 0.937744    
## vowelae:LP           -3.060e-02  5.040e-02  -0.607 0.543880    
## voweli:LP            -5.225e-02  3.705e-02  -1.410 0.158534    
## vowelu:LP            -1.557e-01  3.586e-02  -4.342 1.46e-05 ***
## vowela:LD             3.679e-03  2.078e-02   0.177 0.859448    
## vowelae:LD            1.727e-02  2.251e-02   0.767 0.443104    
## voweli:LD             3.772e-02  1.717e-02   2.197 0.028125 *  
## vowelu:LD             1.695e-03  2.014e-02   0.084 0.932918    
## vowela:TCX            7.787e-02  1.457e-01   0.534 0.593092    
## vowelae:TCX           1.121e-02  7.504e-02   0.149 0.881286    
## voweli:TCX           -8.348e-02  5.104e-02  -1.636 0.102010    
## vowelu:TCX           -3.939e-01  6.559e-02  -6.005 2.15e-09 ***
## vowela:TCY            1.267e-01  9.232e-02   1.372 0.170189    
## vowelae:TCY           1.268e-03  6.085e-02   0.021 0.983373    
## voweli:TCY           -4.132e-03  5.189e-02  -0.080 0.936536    
## vowelu:TCY            2.171e-01  4.907e-02   4.425 9.99e-06 ***
## vowela:TTX           -1.908e-02  2.464e-02  -0.774 0.438837    
## vowelae:TTX          -2.165e-02  2.379e-02  -0.910 0.362824    
## voweli:TTX           -4.989e-03  2.020e-02  -0.247 0.804948    
## vowelu:TTX           -2.790e-02  2.295e-02  -1.216 0.224183    
## vowela:TTY           -1.044e-02  2.627e-02  -0.397 0.691090    
## vowelae:TTY           5.726e-02  3.696e-02   1.549 0.121473    
## voweli:TTY           -1.306e-03  2.215e-02  -0.059 0.952990    
## vowelu:TTY           -1.619e-01  1.966e-02  -8.231 2.76e-16 ***
## vowela:TBX            8.196e-03  1.395e-02   0.588 0.556790    
## vowelae:TBX           1.793e-02  2.221e-02   0.807 0.419519    
## voweli:TBX            4.983e-02  2.140e-02   2.328 0.019959 *  
## vowelu:TBX           -3.532e-03  1.609e-02  -0.219 0.826278    
## vowela:TBY            6.063e-02  2.398e-02   2.529 0.011501 *  
## vowelae:TBY           8.877e-02  4.108e-02   2.161 0.030759 *  
## voweli:TBY            1.236e-01  4.082e-02   3.027 0.002490 ** 
## vowelu:TBY           -2.704e-02  2.419e-02  -1.118 0.263764    
## vowela:hyoidX         1.996e-01  5.850e-02   3.412 0.000654 ***
## vowelae:hyoidX       -6.450e-02  5.544e-02  -1.164 0.244714    
## voweli:hyoidX        -1.791e-01  4.852e-02  -3.691 0.000227 ***
## vowelu:hyoidX        -1.065e-01  4.265e-02  -2.496 0.012604 *  
## vowela:hyoidY        -7.595e-02  1.261e-01  -0.602 0.547055    
## vowelae:hyoidY        7.848e-02  1.392e-01   0.564 0.572872    
## voweli:hyoidY        -1.557e-01  1.247e-01  -1.249 0.211904    
## vowelu:hyoidY        -4.053e-01  1.193e-01  -3.398 0.000688 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2669 on 2928 degrees of freedom
## Multiple R-squared:  0.3728, Adjusted R-squared:  0.3576 
## F-statistic: 24.51 on 71 and 2928 DF,  p-value: < 2.2e-16

F5

##                      Df Sum Sq Mean Sq  F value   Pr(>F)    
## VTRatio               1  79.60   79.60 2272.640  < 2e-16 ***
## I(VTRatio^2)          1  67.90   67.90 1938.537  < 2e-16 ***
## vowel                 4 101.02   25.25  721.020  < 2e-16 ***
## JA                    1   0.25    0.25    6.995 0.008216 ** 
## LP                    1   3.83    3.83  109.474  < 2e-16 ***
## LD                    1   1.50    1.50   42.726 7.40e-11 ***
## TCX                   1   7.16    7.16  204.316  < 2e-16 ***
## TCY                   1   0.81    0.81   23.012 1.69e-06 ***
## TTX                   1   0.00    0.00    0.071 0.789707    
## TTY                   1   8.82    8.82  251.815  < 2e-16 ***
## TBX                   1   0.75    0.75   21.413 3.86e-06 ***
## TBY                   1   0.40    0.40   11.299 0.000785 ***
## hyoidX                1   0.11    0.11    3.008 0.082972 .  
## hyoidY                1   0.21    0.21    5.893 0.015261 *  
## replication           1   0.07    0.07    1.896 0.168641    
## generation            1   1.81    1.81   51.561 8.76e-13 ***
## VTRatio:vowel         4  27.92    6.98  199.314  < 2e-16 ***
## I(VTRatio^2):vowel    4  69.25   17.31  494.260  < 2e-16 ***
## vowel:JA              4   1.22    0.31    8.740 5.19e-07 ***
## vowel:LP              4   1.15    0.29    8.199 1.43e-06 ***
## vowel:LD              4   1.88    0.47   13.422 7.67e-11 ***
## vowel:TCX             4   5.52    1.38   39.389  < 2e-16 ***
## vowel:TCY             4   1.42    0.35   10.119 3.91e-08 ***
## vowel:TTX             4   0.55    0.14    3.933 0.003455 ** 
## vowel:TTY             4   6.81    1.70   48.633  < 2e-16 ***
## vowel:TBX             4   0.23    0.06    1.631 0.163630    
## vowel:TBY             4   1.66    0.42   11.862 1.47e-09 ***
## vowel:hyoidX          4   0.21    0.05    1.464 0.210531    
## vowel:hyoidY          4   0.59    0.15    4.246 0.001984 ** 
## Residuals          2928 102.55    0.04                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f5.m0)
## 
## $vowel
##                 diff          lwr         upr     p adj
## a-schwa   0.03397099  0.004478583  0.06346339 0.0145262
## ae-schwa  0.11405633  0.084563926  0.14354874 0.0000000
## i-schwa  -0.01635768 -0.045850090  0.01313472 0.5534593
## u-schwa  -0.41145974 -0.440952147 -0.38196734 0.0000000
## ae-a      0.08008534  0.050592937  0.10957775 0.0000000
## i-a      -0.05032867 -0.079821079 -0.02083627 0.0000328
## u-a      -0.44543073 -0.474923135 -0.41593832 0.0000000
## i-ae     -0.13041402 -0.159906422 -0.10092161 0.0000000
## u-ae     -0.52551607 -0.555008478 -0.49602367 0.0000000
## u-i      -0.39510206 -0.424594462 -0.36560965 0.0000000
## 
## Call:
## lm(formula = F5 ~ VTRatio + I(VTRatio^2) + vowel + JA + LP + 
##     LD + TCX + TCY + TTX + TTY + TBX + TBY + hyoidX + hyoidY + 
##     (VTRatio:vowel) + (I(VTRatio^2):vowel) + (JA:vowel) + (LP:vowel) + 
##     (LD:vowel) + (TCX:vowel) + (TCY:vowel) + (TTX:vowel) + (TTY:vowel) + 
##     (TBX:vowel) + (TBY:vowel) + (hyoidX:vowel) + (hyoidY:vowel) + 
##     replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.32066 -0.08344  0.00499  0.07665  1.35866 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           2.338e+01  2.150e+00  10.877  < 2e-16 ***
## VTRatio              -2.572e+01  7.811e+00  -3.293 0.001003 ** 
## I(VTRatio^2)          3.084e+01  7.878e+00   3.915 9.26e-05 ***
## vowela                4.063e+00  2.791e+00   1.456 0.145593    
## vowelae               2.927e+00  3.014e+00   0.971 0.331668    
## voweli               -8.532e-01  2.715e+00  -0.314 0.753381    
## vowelu                4.235e+01  2.576e+00  16.438  < 2e-16 ***
## JA                   -1.609e-02  5.344e-03  -3.010 0.002634 ** 
## LP                   -4.765e-02  1.920e-02  -2.482 0.013121 *  
## LD                    1.802e-02  9.168e-03   1.965 0.049487 *  
## TCX                   3.810e-02  3.376e-02   1.129 0.259175    
## TCY                  -3.093e-02  2.133e-02  -1.450 0.147237    
## TTX                   9.831e-03  1.143e-02   0.860 0.389771    
## TTY                  -3.762e-02  1.032e-02  -3.646 0.000271 ***
## TBX                  -1.399e-02  5.704e-03  -2.452 0.014246 *  
## TBY                  -3.592e-02  9.959e-03  -3.607 0.000315 ***
## hyoidX               -4.116e-02  2.051e-02  -2.007 0.044888 *  
## hyoidY                5.569e-02  6.080e-02   0.916 0.359796    
## replication          -5.776e-05  1.192e-04  -0.484 0.628140    
## generation           -5.623e-05  4.036e-05  -1.393 0.163631    
## VTRatio:vowela       -2.904e+01  1.018e+01  -2.854 0.004351 ** 
## VTRatio:vowelae      -2.301e+01  1.101e+01  -2.089 0.036781 *  
## VTRatio:voweli        6.461e+00  1.011e+01   0.639 0.522895    
## VTRatio:vowelu       -2.003e+02  9.240e+00 -21.675  < 2e-16 ***
## I(VTRatio^2):vowela   3.956e+01  1.044e+01   3.788 0.000155 ***
## I(VTRatio^2):vowelae  3.273e+01  1.132e+01   2.893 0.003848 ** 
## I(VTRatio^2):voweli  -7.383e+00  1.040e+01  -0.710 0.477656    
## I(VTRatio^2):vowelu   2.285e+02  9.325e+00  24.505  < 2e-16 ***
## vowela:JA             2.638e-02  9.900e-03   2.665 0.007743 ** 
## vowelae:JA            3.167e-02  1.385e-02   2.287 0.022262 *  
## voweli:JA             1.397e-02  8.290e-03   1.685 0.092045 .  
## vowelu:JA             2.404e-02  6.754e-03   3.559 0.000378 ***
## vowela:LP             3.294e-02  3.016e-02   1.092 0.274897    
## vowelae:LP            9.302e-02  3.534e-02   2.632 0.008527 ** 
## voweli:LP            -1.265e-02  2.598e-02  -0.487 0.626204    
## vowelu:LP            -1.600e-02  2.514e-02  -0.636 0.524514    
## vowela:LD            -2.885e-02  1.457e-02  -1.981 0.047726 *  
## vowelae:LD           -5.432e-02  1.578e-02  -3.441 0.000587 ***
## voweli:LD             1.269e-02  1.204e-02   1.054 0.292149    
## vowelu:LD             4.541e-04  1.412e-02   0.032 0.974347    
## vowela:TCX           -3.512e-01  1.022e-01  -3.437 0.000596 ***
## vowelae:TCX           5.881e-02  5.261e-02   1.118 0.263753    
## voweli:TCX           -8.129e-02  3.579e-02  -2.272 0.023188 *  
## vowelu:TCX            3.005e-01  4.599e-02   6.535 7.48e-11 ***
## vowela:TCY           -4.300e-01  6.473e-02  -6.643 3.65e-11 ***
## vowelae:TCY          -1.836e-04  4.267e-02  -0.004 0.996566    
## voweli:TCY           -2.311e-02  3.638e-02  -0.635 0.525275    
## vowelu:TCY           -4.835e-02  3.441e-02  -1.405 0.160034    
## vowela:TTX           -1.347e-02  1.728e-02  -0.779 0.435861    
## vowelae:TTX           7.176e-03  1.668e-02   0.430 0.667070    
## voweli:TTX           -8.159e-03  1.416e-02  -0.576 0.564634    
## vowelu:TTX           -2.683e-02  1.609e-02  -1.668 0.095489 .  
## vowela:TTY           -4.608e-02  1.842e-02  -2.502 0.012405 *  
## vowelae:TTY          -9.439e-02  2.592e-02  -3.642 0.000275 ***
## voweli:TTY            7.410e-02  1.553e-02   4.772 1.91e-06 ***
## vowelu:TTY           -1.096e-01  1.379e-02  -7.948 2.67e-15 ***
## vowela:TBX            1.983e-02  9.778e-03   2.028 0.042610 *  
## vowelae:TBX          -4.275e-02  1.557e-02  -2.745 0.006089 ** 
## voweli:TBX            1.472e-02  1.501e-02   0.981 0.326749    
## vowelu:TBX           -1.336e-02  1.128e-02  -1.184 0.236381    
## vowela:TBY            6.635e-02  1.681e-02   3.947 8.11e-05 ***
## vowelae:TBY          -8.711e-02  2.880e-02  -3.025 0.002510 ** 
## voweli:TBY            1.957e-03  2.862e-02   0.068 0.945476    
## vowelu:TBY            1.005e-02  1.696e-02   0.593 0.553481    
## vowela:hyoidX        -5.864e-02  4.102e-02  -1.430 0.152948    
## vowelae:hyoidX        1.681e-02  3.887e-02   0.433 0.665378    
## voweli:hyoidX         9.292e-03  3.402e-02   0.273 0.784771    
## vowelu:hyoidX        -3.109e-02  2.991e-02  -1.039 0.298684    
## vowela:hyoidY         5.661e-02  8.842e-02   0.640 0.522079    
## vowelae:hyoidY       -1.986e-01  9.759e-02  -2.035 0.041950 *  
## voweli:hyoidY         6.354e-02  8.743e-02   0.727 0.467412    
## vowelu:hyoidY        -1.962e-01  8.363e-02  -2.346 0.019042 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1872 on 2928 degrees of freedom
## Multiple R-squared:  0.7929, Adjusted R-squared:  0.7879 
## F-statistic: 157.9 on 71 and 2928 DF,  p-value: < 2.2e-16
##                      Df Sum Sq Mean Sq  F value   Pr(>F)    
## VTRatio               1   81.8   81.85 1074.541  < 2e-16 ***
## I(VTRatio^2)          1  148.6  148.56 1950.414  < 2e-16 ***
## vowel                 4  376.8   94.20 1236.675  < 2e-16 ***
## JA                    1    0.0    0.00    0.006 0.940643    
## LP                    1    9.6    9.64  126.517  < 2e-16 ***
## LD                    1    8.9    8.93  117.177  < 2e-16 ***
## TCX                   1   68.3   68.31  896.760  < 2e-16 ***
## TCY                   1    1.0    0.97   12.744 0.000363 ***
## TTX                   1    0.5    0.45    5.936 0.014891 *  
## TTY                   1   12.9   12.86  168.791  < 2e-16 ***
## TBX                   1    0.9    0.94   12.276 0.000466 ***
## TBY                   1    0.2    0.18    2.422 0.119712    
## hyoidX                1    0.4    0.36    4.741 0.029523 *  
## hyoidY                1    0.4    0.38    4.955 0.026095 *  
## replication           1    0.2    0.16    2.151 0.142620    
## generation            1    4.4    4.42   58.088 3.36e-14 ***
## VTRatio:vowel         4  192.6   48.15  632.139  < 2e-16 ***
## I(VTRatio^2):vowel    4  276.1   69.02  906.195  < 2e-16 ***
## vowel:JA              4    1.0    0.26    3.382 0.009071 ** 
## vowel:LP              4    0.1    0.03    0.374 0.827099    
## vowel:LD              4    1.3    0.33    4.293 0.001827 ** 
## vowel:TCX             4    5.3    1.31   17.237 5.52e-14 ***
## vowel:TCY             4    1.2    0.29    3.789 0.004458 ** 
## vowel:TTX             4    0.4    0.09    1.184 0.315538    
## vowel:TTY             4    6.4    1.59   20.915  < 2e-16 ***
## vowel:TBX             4    0.4    0.09    1.198 0.309705    
## vowel:TBY             4    0.4    0.10    1.292 0.270808    
## vowel:hyoidX          4    0.4    0.09    1.187 0.314407    
## vowel:hyoidY          4    1.5    0.37    4.835 0.000691 ***
## Residuals          2928  223.0    0.08                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f5e.m0)
## 
## $vowel
##                diff          lwr        upr     p adj
## a-schwa  0.03120784 -0.012284229 0.07469991 0.2867937
## ae-schwa 0.05022266  0.006730591 0.09371473 0.0141603
## i-schwa  0.07725026  0.033758190 0.12074233 0.0000130
## u-schwa  0.92289511  0.879403041 0.96638718 0.0000000
## ae-a     0.01901482 -0.024477249 0.06250689 0.7552733
## i-a      0.04604242  0.002550350 0.08953449 0.0317617
## u-a      0.89168727  0.848195201 0.93517934 0.0000000
## i-ae     0.02702760 -0.016464470 0.07051967 0.4364064
## u-ae     0.87267245  0.829180381 0.91616452 0.0000000
## u-i      0.84564485  0.802152782 0.88913692 0.0000000
## 
## Call:
## lm(formula = F5.error ~ VTRatio + I(VTRatio^2) + vowel + JA + 
##     LP + LD + TCX + TCY + TTX + TTY + TBX + TBY + hyoidX + hyoidY + 
##     (VTRatio:vowel) + (I(VTRatio^2):vowel) + (JA:vowel) + (LP:vowel) + 
##     (LD:vowel) + (TCX:vowel) + (TCY:vowel) + (TTX:vowel) + (TTY:vowel) + 
##     (TBX:vowel) + (TBY:vowel) + (hyoidX:vowel) + (hyoidY:vowel) + 
##     replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.75728 -0.04317 -0.00404  0.03637  2.27014 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           2.827e+00  3.170e+00   0.892 0.372587    
## VTRatio              -1.541e+01  1.152e+01  -1.338 0.180983    
## I(VTRatio^2)          1.895e+01  1.162e+01   1.631 0.103053    
## vowela                5.091e+00  4.116e+00   1.237 0.216215    
## vowelae               4.001e+00  4.445e+00   0.900 0.368185    
## voweli                3.897e+00  4.004e+00   0.973 0.330478    
## vowelu                9.756e+01  3.799e+00  25.678  < 2e-16 ***
## JA                   -1.105e-02  7.881e-03  -1.402 0.161045    
## LP                   -3.511e-02  2.831e-02  -1.240 0.215046    
## LD                    6.146e-03  1.352e-02   0.455 0.649464    
## TCX                   9.089e-02  4.979e-02   1.825 0.068031 .  
## TCY                  -4.333e-03  3.146e-02  -0.138 0.890458    
## TTX                   1.514e-02  1.685e-02   0.898 0.369136    
## TTY                  -1.062e-02  1.522e-02  -0.698 0.485203    
## TBX                  -7.466e-03  8.411e-03  -0.888 0.374843    
## TBY                  -7.470e-03  1.469e-02  -0.509 0.611025    
## hyoidX               -3.344e-02  3.025e-02  -1.105 0.269078    
## hyoidY               -4.125e-02  8.966e-02  -0.460 0.645471    
## replication          -1.741e-04  1.758e-04  -0.990 0.322147    
## generation           -1.633e-04  5.951e-05  -2.743 0.006119 ** 
## VTRatio:vowela       -2.577e+01  1.501e+01  -1.717 0.086075 .  
## VTRatio:vowelae      -2.413e+01  1.624e+01  -1.486 0.137428    
## VTRatio:voweli       -1.297e+01  1.491e+01  -0.869 0.384687    
## VTRatio:vowelu       -4.308e+02  1.363e+01 -31.616  < 2e-16 ***
## I(VTRatio^2):vowela   3.101e+01  1.540e+01   2.013 0.044174 *  
## I(VTRatio^2):vowelae  3.007e+01  1.669e+01   1.802 0.071665 .  
## I(VTRatio^2):voweli   1.301e+01  1.533e+01   0.849 0.396213    
## I(VTRatio^2):vowelu   4.854e+02  1.375e+01  35.297  < 2e-16 ***
## vowela:JA             1.606e-02  1.460e-02   1.100 0.271516    
## vowelae:JA            7.121e-03  2.042e-02   0.349 0.727317    
## voweli:JA             1.735e-02  1.223e-02   1.419 0.155967    
## vowelu:JA             3.274e-02  9.960e-03   3.287 0.001023 ** 
## vowela:LP             2.083e-02  4.448e-02   0.468 0.639528    
## vowelae:LP            7.210e-03  5.211e-02   0.138 0.889975    
## voweli:LP            -1.674e-02  3.831e-02  -0.437 0.662105    
## vowelu:LP            -2.840e-03  3.707e-02  -0.077 0.938949    
## vowela:LD            -1.393e-02  2.148e-02  -0.648 0.516788    
## vowelae:LD           -1.047e-02  2.328e-02  -0.450 0.652818    
## voweli:LD             2.592e-02  1.776e-02   1.460 0.144436    
## vowelu:LD             5.421e-02  2.082e-02   2.604 0.009270 ** 
## vowela:TCX           -1.005e-01  1.507e-01  -0.667 0.504815    
## vowelae:TCX           5.273e-02  7.759e-02   0.680 0.496792    
## voweli:TCX           -1.014e-01  5.277e-02  -1.921 0.054813 .  
## vowelu:TCX            4.224e-01  6.782e-02   6.229 5.38e-10 ***
## vowela:TCY           -1.620e-01  9.545e-02  -1.697 0.089819 .  
## vowelae:TCY          -5.688e-03  6.292e-02  -0.090 0.927980    
## voweli:TCY           -1.042e-01  5.365e-02  -1.943 0.052101 .  
## vowelu:TCY           -1.784e-01  5.074e-02  -3.517 0.000444 ***
## vowela:TTX           -3.302e-02  2.548e-02  -1.296 0.195144    
## vowelae:TTX          -1.655e-02  2.460e-02  -0.673 0.501135    
## voweli:TTX           -1.647e-02  2.089e-02  -0.789 0.430362    
## vowelu:TTX           -4.501e-02  2.373e-02  -1.897 0.057929 .  
## vowela:TTY           -2.439e-02  2.716e-02  -0.898 0.369210    
## vowelae:TTY           1.215e-02  3.822e-02   0.318 0.750553    
## voweli:TTY            1.866e-02  2.290e-02   0.815 0.415212    
## vowelu:TTY           -1.398e-01  2.033e-02  -6.876 7.51e-12 ***
## vowela:TBX            1.201e-02  1.442e-02   0.833 0.405022    
## vowelae:TBX           1.542e-03  2.297e-02   0.067 0.946485    
## voweli:TBX            3.268e-02  2.213e-02   1.477 0.139900    
## vowelu:TBX           -2.522e-02  1.664e-02  -1.516 0.129682    
## vowela:TBY            3.102e-02  2.479e-02   1.251 0.210957    
## vowelae:TBY           5.018e-03  4.247e-02   0.118 0.905961    
## voweli:TBY           -2.799e-03  4.220e-02  -0.066 0.947118    
## vowelu:TBY           -2.104e-02  2.501e-02  -0.841 0.400297    
## vowela:hyoidX        -1.103e-02  6.049e-02  -0.182 0.855331    
## vowelae:hyoidX        2.808e-02  5.732e-02   0.490 0.624260    
## voweli:hyoidX         2.608e-02  5.017e-02   0.520 0.603248    
## vowelu:hyoidX        -8.333e-02  4.410e-02  -1.890 0.058912 .  
## vowela:hyoidY         1.922e-02  1.304e-01   0.147 0.882818    
## vowelae:hyoidY       -1.469e-01  1.439e-01  -1.021 0.307466    
## voweli:hyoidY         1.501e-01  1.289e-01   1.165 0.244278    
## vowelu:hyoidY         3.975e-01  1.233e-01   3.223 0.001282 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.276 on 2928 degrees of freedom
## Multiple R-squared:  0.8435, Adjusted R-squared:  0.8397 
## F-statistic: 222.2 on 71 and 2928 DF,  p-value: < 2.2e-16
Summary of F1–F5 regressions with betas (for non-factor DVs and ‘.’ for factors), p-values, and adjusted R2. Interactions are denoted by ‘:’.
DVs, interactions & R2 F1 F1.err F2 F2.err F3 F3.err F4 F4.err F5 F5.err
VTRatio 10 (0.005**) -3.6 (0.38) -0.4 (0.94) -4.5 (0.55) 1.5e+02 (3.5e-38***) -1.4e+02 (2.1e-22***) 61 (5.9e-11***) -9.3 (0.4) -26 (0.001**) -15 (0.18)
VTRatio^2 -11 (0.0034**) 4 (0.33) -0.032 (1) 5 (0.51) -1.5e+02 (2.6e-40***) 1.5e+02 (1.3e-24***) -61 (1.5e-10***) 11 (0.33) 31 (9.3e-05***) 19 (0.1)
vowel . (0***) . (4.5e-114***) . (0***) . (2.6e-265***) . (0***) . (3.6e-107***) . (0***) . (2.5e-67***) . (0***) . (0***)
JA 0.00097 (0.7) -0.0023 (0.41) -0.0011 (0.76) -0.0035 (0.5) -0.0023 (0.77) 0.0065 (0.51) 0.0046 (0.47) 0.0017 (0.83) -0.016 (0.0026**) -0.011 (0.16)
LP 0.0068 (0.45) 0.0015 (0.88) 0.0037 (0.78) 0.0044 (0.81) -0.02 (0.48) 0.017 (0.62) 0.03 (0.2) 0.0095 (0.73) -0.048 (0.013*) -0.035 (0.22)
LD 0.0015 (0.73) 0.00044 (0.93) -0.0025 (0.7) 1e-05 (1) 0.0084 (0.53) -0.0058 (0.73) -0.018 (0.095) 0.00045 (0.97) 0.018 (0.049*) 0.0061 (0.65)
TCX -0.013 (0.41) 0.0035 (0.84) 0.045 (0.055) 0.0041 (0.9) -0.22 (5.4e-06***) 0.24 (0.00014***) 0.11 (0.0089**) 0.078 (0.11) 0.038 (0.26) 0.091 (0.068)
TCY -0.0035 (0.73) -0.0026 (0.81) -0.015 (0.32) -0.0027 (0.9) -0.064 (0.038*) 0.1 (0.009**) -0.078 (0.0023**) -0.013 (0.68) -0.031 (0.15) -0.0043 (0.89)
TTX -0.0048 (0.37) -0.0021 (0.73) -0.0058 (0.46) -0.0041 (0.71) 0.016 (0.35) -0.00077 (0.97) -0.051 (0.00018***) 0.013 (0.43) 0.0098 (0.39) 0.015 (0.37)
TTY 0.00079 (0.87) -0.0018 (0.73) 0.0044 (0.54) -0.0024 (0.81) 0.012 (0.43) -0.0066 (0.73) -0.02 (0.11) -0.02 (0.17) -0.038 (0.00027***) -0.011 (0.49)
TBX 0.0045 (0.09) 0.00032 (0.92) 0.0026 (0.5) 0.00049 (0.93) 0.03 (0.00036***) -0.028 (0.0071**) 0.018 (0.0074**) -0.018 (0.031*) -0.014 (0.014*) -0.0075 (0.37)
TBY 0.00043 (0.93) 0.00096 (0.85) 0.009 (0.19) 0.00067 (0.94) 0.026 (0.07) -0.032 (0.078) 0.042 (0.00042***) -0.0086 (0.55) -0.036 (0.00032***) -0.0075 (0.61)
hyoidX -0.018 (0.065) -0.0095 (0.38) -0.02 (0.15) -0.018 (0.35) -0.037 (0.21) 0.083 (0.028*) 0.027 (0.27) -0.0053 (0.86) -0.041 (0.045*) -0.033 (0.27)
hyoidY -0.037 (0.2) 0.004 (0.9) 0.032 (0.45) 0.0012 (0.98) -0.11 (0.21) -0.15 (0.18) -0.4 (5.3e-08***) -0.057 (0.51) 0.056 (0.36) -0.041 (0.65)
replication 1.4e-05 (0.81) 7.9e-05 (0.21) 0.00013 (0.13) -0.00015 (0.19) 7.2e-05 (0.68) -3.9e-05 (0.86) 2.7e-05 (0.85) -7.6e-05 (0.66) -5.8e-05 (0.63) -0.00017 (0.32)
generation -0.00014 (8.3e-13***) -0.00016 (2.4e-13***) -6.4e-05 (0.022*) -0.00027 (3.4e-12***) -8.5e-05 (0.15) -4.9e-05 (0.5) -6.1e-05 (0.21) -0.00032 (3.3e-08***) -5.6e-05 (0.16) -0.00016 (0.0061**)
VTRatio:vowel . (4e-149***) . (2.9e-175***) . (1.3e-268***) . (0***) . (1.9e-36***) . (3.9e-125***) . (1.1e-41***) . (3.1e-33***) . (2.4e-151***) . (0***)
VTRatio^2:vowel . (3e-163***) . (2.3e-38***) . (1.6e-263***) . (1.6e-211***) . (3.7e-80***) . (8.4e-48***) . (1.5e-77***) . (9.3e-34***) . (0***) . (0***)
vowel:JA . (6.7e-39***) . (2.5e-16***) . (1.6e-13***) . (0.00023***) . (2.1e-07***) . (8.4e-07***) . (7.4e-10***) . (9.6e-05***) . (5.2e-07***) . (0.0091**)
vowel:LP . (1.3e-53***) . (1.6e-25***) . (9.2e-05***) . (0.1) . (0.0083**) . (2.1e-07***) . (5.4e-10***) . (1.6e-07***) . (1.4e-06***) . (0.83)
vowel:LD . (8.2e-22***) . (3e-08***) . (2.6e-11***) . (0.062) . (0.00023***) . (1.1e-05***) . (0.0026**) . (0.2) . (7.7e-11***) . (0.0018**)
vowel:TCX . (6.3e-71***) . (3.4e-105***) . (1e-35***) . (8.1e-23***) . (0.00013***) . (1.4e-13***) . (5.9e-45***) . (1.5e-21***) . (3.6e-32***) . (5.5e-14***)
vowel:TCY . (2.4e-13***) . (2.2e-05***) . (1.1e-37***) . (1e-28***) . (5.4e-61***) . (4.3e-35***) . (1.8e-37***) . (6.4e-05***) . (3.9e-08***) . (0.0045**)
vowel:TTX . (3.3e-37***) . (5.7e-21***) . (0.22) . (0.56) . (0.77) . (0.026*) . (0.0018**) . (0.43) . (0.0035**) . (0.32)
vowel:TTY . (8.2e-05***) . (0.00086***) . (1.3e-15***) . (0.48) . (2.7e-07***) . (6.5e-31***) . (1.4e-08***) . (3.8e-18***) . (1.2e-39***) . (5.1e-17***)
vowel:TBX . (3.6e-54***) . (0.00094***) . (1.3e-07***) . (0.027*) . (0.29) . (0.092) . (0.89) . (0.17) . (0.16) . (0.31)
vowel:TBY . (5.3e-60***) . (1.3e-08***) . (0.03*) . (0.00013***) . (9.5e-05***) . (0.028*) . (0.15) . (5.5e-05***) . (1.5e-09***) . (0.27)
vowel:hyoidX . (3e-28***) . (0.00063***) . (1.5e-09***) . (8.8e-15***) . (4e-08***) . (3.1e-08***) . (2.5e-38***) . (7.3e-10***) . (0.21) . (0.31)
vowel:hyoidY . (9.9e-11***) . (2.8e-05***) . (5.2e-19***) . (0.16) . (3.2e-29***) . (9.3e-08***) . (1.9e-23***) . (0.0015**) . (0.002**) . (0.00069***)
adjusted R2 99.7% 54.6% 99.8% 70.1% 78.5% 70.6% 69.2% 35.8% 78.8% 84.0%

PC1 – PC3 on VTRatio

## Analysis of Variance Table
## 
## Response: PC1
##                      Df Sum Sq Mean Sq    F value Pr(>F)    
## VTRatio               1 7241.1  7241.1 29299.1232 <2e-16 ***
## I(VTRatio^2)          1  139.8   139.8   565.8072 <2e-16 ***
## vowel                 4 6339.7  1584.9  6413.0481 <2e-16 ***
## replication           1    0.0     0.0     0.1272 0.7213    
## generation            1    0.1     0.1     0.3635 0.5466    
## VTRatio:vowel         4  165.7    41.4   167.6186 <2e-16 ***
## I(VTRatio^2):vowel    4   45.6    11.4    46.0959 <2e-16 ***
## Residuals          2983  737.2     0.2                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = pc1.m0)
## 
## $vowel
##                diff        lwr        upr p adj
## a-schwa  -1.1031824 -1.1815231 -1.0248417     0
## ae-schwa -0.5990499 -0.6773906 -0.5207092     0
## i-schwa   2.9375638  2.8592231  3.0159045     0
## u-schwa   1.2665702  1.1882295  1.3449109     0
## ae-a      0.5041325  0.4257918  0.5824732     0
## i-a       4.0407462  3.9624055  4.1190869     0
## u-a       2.3697526  2.2914119  2.4480933     0
## i-ae      3.5366137  3.4582730  3.6149543     0
## u-ae      1.8656200  1.7872793  1.9439607     0
## u-i      -1.6709936 -1.7493343 -1.5926529     0
## 
## Call:
## lm(formula = PC1 ~ VTRatio + I(VTRatio^2) + +vowel + replication + 
##     generation + (VTRatio:vowel) + (I(VTRatio^2):vowel), data = d)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.7582 -0.2392  0.0088  0.2499  2.5021 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          -5.461e+01  2.331e+00 -23.426  < 2e-16 ***
## VTRatio               2.009e+02  1.032e+01  19.468  < 2e-16 ***
## I(VTRatio^2)         -1.781e+02  1.135e+01 -15.692  < 2e-16 ***
## vowela               -1.601e+00  3.357e+00  -0.477  0.63351    
## vowelae               9.443e+00  3.792e+00   2.490  0.01282 *  
## voweli                1.264e+01  3.209e+00   3.938 8.39e-05 ***
## vowelu                4.154e+01  3.295e+00  12.605  < 2e-16 ***
## replication           1.152e-04  3.145e-04   0.366  0.71419    
## generation           -9.743e-05  9.615e-05  -1.013  0.31103    
## VTRatio:vowela       -3.017e+00  1.486e+01  -0.203  0.83912    
## VTRatio:vowelae      -4.304e+01  1.668e+01  -2.580  0.00993 ** 
## VTRatio:voweli       -3.187e+01  1.422e+01  -2.242  0.02504 *  
## VTRatio:vowelu       -1.748e+02  1.461e+01 -11.966  < 2e-16 ***
## I(VTRatio^2):vowela   8.991e+00  1.632e+01   0.551  0.58172    
## I(VTRatio^2):vowelae  4.558e+01  1.822e+01   2.502  0.01239 *  
## I(VTRatio^2):voweli   2.277e+01  1.563e+01   1.457  0.14517    
## I(VTRatio^2):vowelu   1.879e+02  1.606e+01  11.696  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4971 on 2983 degrees of freedom
## Multiple R-squared:  0.9497, Adjusted R-squared:  0.9495 
## F-statistic:  3523 on 16 and 2983 DF,  p-value: < 2.2e-16
## Analysis of Variance Table
## 
## Response: PC2
##                      Df Sum Sq Mean Sq    F value Pr(>F)    
## VTRatio               1 3477.7  3477.7 17692.5120 <2e-16 ***
## I(VTRatio^2)          1   99.6    99.6   506.7095 <2e-16 ***
## vowel                 4 4951.9  1238.0  6298.1042 <2e-16 ***
## replication           1    0.0     0.0     0.0394 0.8427    
## generation            1    0.0     0.0     0.0762 0.7825    
## VTRatio:vowel         4  170.0    42.5   216.1946 <2e-16 ***
## I(VTRatio^2):vowel    4   73.1    18.3    92.9150 <2e-16 ***
## Residuals          2983  586.3     0.2                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = pc2.m0)
## 
## $vowel
##                diff        lwr        upr p adj
## a-schwa   1.1021647  1.0322988  1.1720306     0
## ae-schwa  1.3550032  1.2851373  1.4248690     0
## i-schwa  -1.1622519 -1.2321178 -1.0923860     0
## u-schwa  -1.9825271 -2.0523929 -1.9126612     0
## ae-a      0.2528385  0.1829726  0.3227043     0
## i-a      -2.2644166 -2.3342825 -2.1945507     0
## u-a      -3.0846918 -3.1545576 -3.0148259     0
## i-ae     -2.5172551 -2.5871209 -2.4473892     0
## u-ae     -3.3375303 -3.4073961 -3.2676644     0
## u-i      -0.8202752 -0.8901410 -0.7504093     0
## 
## Call:
## lm(formula = PC2 ~ VTRatio + I(VTRatio^2) + +vowel + replication + 
##     generation + (VTRatio:vowel) + (I(VTRatio^2):vowel), data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.80923 -0.28804 -0.00761  0.27579  2.08833 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           1.109e+01  2.079e+00   5.337 1.02e-07 ***
## VTRatio              -6.458e+01  9.204e+00  -7.016 2.81e-12 ***
## I(VTRatio^2)          8.830e+01  1.012e+01   8.725  < 2e-16 ***
## vowela               -1.248e+01  2.994e+00  -4.168 3.15e-05 ***
## vowelae              -8.715e+00  3.382e+00  -2.577 0.010016 *  
## voweli               -7.310e+00  2.862e+00  -2.554 0.010697 *  
## vowelu                3.069e+01  2.939e+00  10.441  < 2e-16 ***
## replication          -7.149e-05  2.805e-04  -0.255 0.798841    
## generation            1.699e-04  8.575e-05   1.981 0.047675 *  
## VTRatio:vowela        5.586e+01  1.325e+01   4.215 2.57e-05 ***
## VTRatio:vowelae       3.705e+01  1.488e+01   2.490 0.012838 *  
## VTRatio:voweli        1.551e+01  1.268e+01   1.223 0.221377    
## VTRatio:vowelu       -1.608e+02  1.303e+01 -12.345  < 2e-16 ***
## I(VTRatio^2):vowela  -5.664e+01  1.455e+01  -3.891 0.000102 ***
## I(VTRatio^2):vowelae -3.242e+01  1.625e+01  -1.995 0.046095 *  
## I(VTRatio^2):voweli  -4.227e+00  1.394e+01  -0.303 0.761699    
## I(VTRatio^2):vowelu   1.941e+02  1.432e+01  13.548  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4434 on 2983 degrees of freedom
## Multiple R-squared:  0.9373, Adjusted R-squared:  0.937 
## F-statistic:  2789 on 16 and 2983 DF,  p-value: < 2.2e-16
## Analysis of Variance Table
## 
## Response: PC3
##                      Df Sum Sq Mean Sq   F value    Pr(>F)    
## VTRatio               1  850.9  850.88 3306.5572 < 2.2e-16 ***
## I(VTRatio^2)          1   22.9   22.93   89.1204 < 2.2e-16 ***
## vowel                 4 6694.0 1673.49 6503.2624 < 2.2e-16 ***
## replication           1    0.0    0.00    0.0003    0.9851    
## generation            1    5.6    5.58   21.6948 3.336e-06 ***
## VTRatio:vowel         4  181.8   45.45  176.6069 < 2.2e-16 ***
## I(VTRatio^2):vowel    4  211.6   52.90  205.5581 < 2.2e-16 ***
## Residuals          2983  767.6    0.26                        
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = pc3.m0)
## 
## $vowel
##                diff        lwr        upr p adj
## a-schwa  -0.4096617 -0.4896009 -0.3297225     0
## ae-schwa  1.3612149  1.2812757  1.4411541     0
## i-schwa   2.5746734  2.4947342  2.6546127     0
## u-schwa  -1.7655791 -1.8455183 -1.6856399     0
## ae-a      1.7708766  1.6909374  1.8508158     0
## i-a       2.9843352  2.9043960  3.0642744     0
## u-a      -1.3559173 -1.4358565 -1.2759781     0
## i-ae      1.2134586  1.1335194  1.2933978     0
## u-ae     -3.1267939 -3.2067332 -3.0468547     0
## u-i      -4.3402525 -4.4201917 -4.2603133     0
## 
## Call:
## lm(formula = PC3 ~ VTRatio + I(VTRatio^2) + +vowel + replication + 
##     generation + (VTRatio:vowel) + (I(VTRatio^2):vowel), data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.69154 -0.31417 -0.03315  0.27797  2.22259 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           1.794e+01  2.379e+00   7.544 6.02e-14 ***
## VTRatio              -5.979e+01  1.053e+01  -5.677 1.50e-08 ***
## I(VTRatio^2)          4.267e+01  1.158e+01   3.685 0.000233 ***
## vowela               -1.847e+01  3.425e+00  -5.392 7.51e-08 ***
## vowelae              -1.639e+01  3.869e+00  -4.235 2.35e-05 ***
## voweli               -6.599e+01  3.275e+00 -20.150  < 2e-16 ***
## vowelu                1.925e+01  3.363e+00   5.723 1.15e-08 ***
## replication          -4.608e-05  3.210e-04  -0.144 0.885845    
## generation           -4.131e-04  9.811e-05  -4.210 2.63e-05 ***
## VTRatio:vowela        7.111e+01  1.516e+01   4.689 2.87e-06 ***
## VTRatio:vowelae       7.417e+01  1.702e+01   4.357 1.37e-05 ***
## VTRatio:voweli        2.913e+02  1.451e+01  20.084  < 2e-16 ***
## VTRatio:vowelu       -1.090e+02  1.491e+01  -7.312 3.36e-13 ***
## I(VTRatio^2):vowela  -6.820e+01  1.665e+01  -4.095 4.33e-05 ***
## I(VTRatio^2):vowelae -7.645e+01  1.859e+01  -4.113 4.02e-05 ***
## I(VTRatio^2):voweli  -3.061e+02  1.595e+01 -19.198  < 2e-16 ***
## I(VTRatio^2):vowelu   1.372e+02  1.639e+01   8.374  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5073 on 2983 degrees of freedom
## Multiple R-squared:  0.9121, Adjusted R-squared:  0.9116 
## F-statistic:  1935 on 16 and 2983 DF,  p-value: < 2.2e-16
Summary of PC1 – PC3 regressions with betas (for non-factor DVs and ‘.’ for factors), p-values, and adjusted R2. Interactions are denoted by ‘:’.
DVs, interactions & R2 PC1 PC2 PC3
VTRatio 2e+02 (1.4e-79***) -65 (2.8e-12***) -60 (1.5e-08***)
VTRatio^2 -1.8e+02 (2.2e-53***) 88 (4.3e-18***) 43 (0.00023***)
vowel . (0***) . (0***) . (0***)
replication 0.00012 (0.71) -7.1e-05 (0.8) -4.6e-05 (0.89)
generation -9.7e-05 (0.31) 0.00017 (0.048*) -0.00041 (2.6e-05***)
VTRatio:vowel . (1.3e-129***) . (4.3e-163***) . (6.1e-136***)
VTRatio^2:vowel . (1.2e-37***) . (1.4e-74***) . (6.6e-156***)
adjusted R2 94.9% 93.7% 91.2%

Overall acoustic error over F1 – F5 on VTRatio

## Analysis of Variance Table
## 
## Response: acoustic.err
##                      Df Sum Sq Mean Sq   F value    Pr(>F)    
## VTRatio               1  77.56   77.56 1889.7671 < 2.2e-16 ***
## I(VTRatio^2)          1 321.43  321.43 7831.8770 < 2.2e-16 ***
## vowel                 4 251.60   62.90 1532.5979 < 2.2e-16 ***
## JA                    1   1.33    1.33   32.4280 1.360e-08 ***
## LP                    1   6.37    6.37  155.1530 < 2.2e-16 ***
## LD                    1   0.81    0.81   19.8182 8.835e-06 ***
## TCX                   1  40.52   40.52  987.3774 < 2.2e-16 ***
## TCY                   1   0.92    0.92   22.3806 2.342e-06 ***
## TTX                   1   0.26    0.26    6.3411 0.0118499 *  
## TTY                   1  24.47   24.47  596.3399 < 2.2e-16 ***
## TBX                   1   8.79    8.79  214.2290 < 2.2e-16 ***
## TBY                   1   0.95    0.95   23.0683 1.642e-06 ***
## hyoidX                1   0.11    0.11    2.6668 0.1025665    
## hyoidY                1   2.93    2.93   71.2920 < 2.2e-16 ***
## replication           1   0.02    0.02    0.5749 0.4483818    
## generation            1   6.66    6.66  162.1519 < 2.2e-16 ***
## VTRatio:vowel         4  60.97   15.24  371.4040 < 2.2e-16 ***
## I(VTRatio^2):vowel    4  24.33    6.08  148.2226 < 2.2e-16 ***
## vowel:JA              4   3.60    0.90   21.9408 < 2.2e-16 ***
## vowel:LP              4   3.07    0.77   18.7013 3.420e-15 ***
## vowel:LD              4   2.41    0.60   14.6600 7.340e-12 ***
## vowel:TCX             4   5.07    1.27   30.8872 < 2.2e-16 ***
## vowel:TCY             4   5.43    1.36   33.0727 < 2.2e-16 ***
## vowel:TTX             4   0.78    0.20    4.7656 0.0007835 ***
## vowel:TTY             4   8.13    2.03   49.5388 < 2.2e-16 ***
## vowel:TBX             4   1.41    0.35    8.5605 7.261e-07 ***
## vowel:TBY             4   5.05    1.26   30.7785 < 2.2e-16 ***
## vowel:hyoidX          4  11.41    2.85   69.5251 < 2.2e-16 ***
## vowel:hyoidY          4   3.63    0.91   22.1150 < 2.2e-16 ***
## Residuals          2928 120.17    0.04                        
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = err.m0)
## 
## $vowel
##                 diff          lwr         upr     p adj
## a-schwa   0.33358475  0.301659677  0.36550982 0.0000000
## ae-schwa  0.23487096  0.202945891  0.26679604 0.0000000
## i-schwa   0.37305786  0.341132792  0.40498294 0.0000000
## u-schwa   0.88228693  0.850361858  0.91421200 0.0000000
## ae-a     -0.09871379 -0.130638859 -0.06678871 0.0000000
## i-a       0.03947311  0.007548042  0.07139819 0.0067073
## u-a       0.54870218  0.516777108  0.58062725 0.0000000
## i-ae      0.13818690  0.106261828  0.17011197 0.0000000
## u-ae      0.64741597  0.615490894  0.67934104 0.0000000
## u-i       0.50922907  0.477303993  0.54115414 0.0000000
## 
## Call:
## lm(formula = acoustic.err ~ VTRatio + I(VTRatio^2) + vowel + 
##     JA + LP + LD + TCX + TCY + TTX + TTY + TBX + TBY + hyoidX + 
##     hyoidY + (VTRatio:vowel) + (I(VTRatio^2):vowel) + (JA:vowel) + 
##     (LP:vowel) + (LD:vowel) + (TCX:vowel) + (TCY:vowel) + (TTX:vowel) + 
##     (TTY:vowel) + (TBX:vowel) + (TBY:vowel) + (hyoidX:vowel) + 
##     (hyoidY:vowel) + replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.24376 -0.11844 -0.01663  0.10531  1.12068 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           3.236e+01  2.327e+00  13.904  < 2e-16 ***
## VTRatio              -1.444e+02  8.455e+00 -17.081  < 2e-16 ***
## I(VTRatio^2)          1.578e+02  8.528e+00  18.506  < 2e-16 ***
## vowela                1.699e+01  3.021e+00   5.624 2.04e-08 ***
## vowelae               1.650e+01  3.263e+00   5.056 4.55e-07 ***
## voweli                2.123e+01  2.939e+00   7.223 6.44e-13 ***
## vowelu                3.595e+01  2.789e+00  12.890  < 2e-16 ***
## JA                   -3.109e-03  5.785e-03  -0.537 0.591041    
## LP                   -1.125e-02  2.078e-02  -0.541 0.588470    
## LD                   -1.213e-03  9.925e-03  -0.122 0.902752    
## TCX                   3.698e-01  3.655e-02  10.117  < 2e-16 ***
## TCY                  -8.133e-03  2.309e-02  -0.352 0.724698    
## TTX                   1.544e-03  1.237e-02   0.125 0.900719    
## TTY                  -6.464e-02  1.117e-02  -5.787 7.90e-09 ***
## TBX                  -5.854e-02  6.174e-03  -9.481  < 2e-16 ***
## TBY                  -4.840e-02  1.078e-02  -4.490 7.41e-06 ***
## hyoidX                8.416e-03  2.221e-02   0.379 0.704740    
## hyoidY               -1.949e-01  6.582e-02  -2.962 0.003082 ** 
## replication          -1.452e-04  1.291e-04  -1.125 0.260615    
## generation           -3.584e-04  4.368e-05  -8.203 3.46e-16 ***
## VTRatio:vowela       -5.195e+01  1.102e+01  -4.716 2.52e-06 ***
## VTRatio:vowelae      -5.886e+01  1.192e+01  -4.936 8.40e-07 ***
## VTRatio:voweli       -7.905e+01  1.095e+01  -7.221 6.53e-13 ***
## VTRatio:vowelu       -1.492e+02  1.000e+01 -14.918  < 2e-16 ***
## I(VTRatio^2):vowela   4.392e+01  1.131e+01   3.885 0.000105 ***
## I(VTRatio^2):vowelae  5.682e+01  1.225e+01   4.639 3.66e-06 ***
## I(VTRatio^2):voweli   7.793e+01  1.125e+01   6.925 5.34e-12 ***
## I(VTRatio^2):vowelu   1.670e+02  1.009e+01  16.549  < 2e-16 ***
## vowela:JA             5.268e-03  1.072e-02   0.492 0.623066    
## vowelae:JA           -1.523e-02  1.499e-02  -1.016 0.309786    
## voweli:JA             1.792e-02  8.974e-03   1.997 0.045950 *  
## vowelu:JA             2.514e-02  7.311e-03   3.439 0.000592 ***
## vowela:LP            -1.428e-02  3.265e-02  -0.437 0.661897    
## vowelae:LP           -3.381e-02  3.825e-02  -0.884 0.376902    
## voweli:LP            -1.079e-01  2.812e-02  -3.839 0.000126 ***
## vowelu:LP            -1.915e-01  2.721e-02  -7.037 2.43e-12 ***
## vowela:LD             2.007e-02  1.577e-02   1.272 0.203304    
## vowelae:LD            2.406e-02  1.709e-02   1.408 0.159238    
## voweli:LD             4.740e-02  1.303e-02   3.636 0.000281 ***
## vowelu:LD             6.896e-02  1.528e-02   4.512 6.68e-06 ***
## vowela:TCX            9.633e-01  1.106e-01   8.710  < 2e-16 ***
## vowelae:TCX          -1.371e-01  5.695e-02  -2.408 0.016113 *  
## voweli:TCX           -2.627e-01  3.874e-02  -6.782 1.43e-11 ***
## vowelu:TCX           -1.727e-01  4.978e-02  -3.469 0.000529 ***
## vowela:TCY            7.046e-01  7.007e-02  10.055  < 2e-16 ***
## vowelae:TCY          -1.264e-02  4.619e-02  -0.274 0.784300    
## voweli:TCY            1.008e-01  3.938e-02   2.560 0.010529 *  
## vowelu:TCY           -9.787e-02  3.724e-02  -2.628 0.008639 ** 
## vowela:TTX           -3.732e-02  1.870e-02  -1.995 0.046086 *  
## vowelae:TTX          -1.523e-02  1.806e-02  -0.843 0.399106    
## voweli:TTX           -5.401e-03  1.533e-02  -0.352 0.724659    
## vowelu:TTX            4.173e-02  1.742e-02   2.396 0.016639 *  
## vowela:TTY            1.267e-01  1.994e-02   6.357 2.38e-10 ***
## vowelae:TTY           1.315e-01  2.805e-02   4.686 2.91e-06 ***
## voweli:TTY            5.986e-02  1.681e-02   3.561 0.000375 ***
## vowelu:TTY           -1.244e-01  1.493e-02  -8.336  < 2e-16 ***
## vowela:TBX            5.932e-02  1.058e-02   5.604 2.28e-08 ***
## vowelae:TBX           2.019e-02  1.686e-02   1.197 0.231218    
## voweli:TBX            1.039e-01  1.624e-02   6.396 1.85e-10 ***
## vowelu:TBX            1.361e-02  1.221e-02   1.115 0.265093    
## vowela:TBY            2.034e-01  1.820e-02  11.179  < 2e-16 ***
## vowelae:TBY           6.141e-02  3.118e-02   1.970 0.048965 *  
## voweli:TBY            2.234e-01  3.098e-02   7.211 7.04e-13 ***
## vowelu:TBY            3.482e-02  1.836e-02   1.896 0.058008 .  
## vowela:hyoidX         5.092e-01  4.440e-02  11.469  < 2e-16 ***
## vowelae:hyoidX       -7.285e-02  4.208e-02  -1.731 0.083509 .  
## voweli:hyoidX        -3.540e-01  3.683e-02  -9.612  < 2e-16 ***
## vowelu:hyoidX        -9.430e-02  3.237e-02  -2.913 0.003608 ** 
## vowela:hyoidY        -2.352e-01  9.572e-02  -2.457 0.014062 *  
## vowelae:hyoidY        4.056e-01  1.056e-01   3.840 0.000126 ***
## voweli:hyoidY         4.295e-01  9.464e-02   4.539 5.88e-06 ***
## vowelu:hyoidY         4.965e-01  9.053e-02   5.485 4.49e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2026 on 2928 degrees of freedom
## Multiple R-squared:  0.8799, Adjusted R-squared:  0.8769 
## F-statistic:   302 on 71 and 2928 DF,  p-value: < 2.2e-16
Summary of F1-F5 error regressions with betas (for non-factor DVs and ‘.’ for factors), p-values, and adjusted R2. Interactions are denoted by ‘:’.
DVs, interactions & R2 F1-F5.err
VTRatio -1.4e+02 (2e-62***)
VTRatio^2 1.6e+02 (2.1e-72***)
vowel . (0***)
JA -0.0031 (0.59)
LP -0.011 (0.59)
LD -0.0012 (0.9)
TCX 0.37 (1.1e-23***)
TCY -0.0081 (0.72)
TTX 0.0015 (0.9)
TTY -0.065 (7.9e-09***)
TBX -0.059 (5e-21***)
TBY -0.048 (7.4e-06***)
hyoidX 0.0084 (0.7)
hyoidY -0.19 (0.0031**)
replication -0.00015 (0.26)
generation -0.00036 (3.5e-16***)
VTRatio:vowel . (5.9e-259***)
VTRatio^2:vowel . (1.4e-115***)
vowel:JA . (7.3e-18***)
vowel:LP . (3.4e-15***)
vowel:LD . (7.3e-12***)
vowel:TCX . (3.2e-25***)
vowel:TCY . (5.1e-27***)
vowel:TTX . (0.00078***)
vowel:TTY . (2.2e-40***)
vowel:TBX . (7.3e-07***)
vowel:TBY . (3.9e-25***)
vowel:hyoidX . (2.6e-56***)
vowel:hyoidY . (5.2e-18***)
adjusted R2 87.7%

## Analysis of Variance Table
## 
## Response: acoustic.err
##                      Df Sum Sq Mean Sq   F value Pr(>F)    
## vowel                 4 255.48   63.87  864.5190 <2e-16 ***
## VTRatio               1  67.94   67.94  919.5902 <2e-16 ***
## I(VTRatio^2)          1 327.18  327.18 4428.6526 <2e-16 ***
## replication           1   0.00    0.00    0.0121 0.9126    
## vowel:VTRatio         4  77.46   19.36  262.1142 <2e-16 ***
## vowel:I(VTRatio^2)    4  51.70   12.93  174.9597 <2e-16 ***
## Residuals          2984 220.45    0.07                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## VTRatio
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## I(VTRatio^2)
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## replication
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## vowel, VTRatio
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## vowel, I(VTRatio^2)
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = lm.euclid.dist)
## 
## $vowel
##                 diff          lwr         upr     p adj
## a-schwa   0.31471076  0.271878392  0.35754314 0.0000000
## ae-schwa  0.17299662  0.130164251  0.21582900 0.0000000
## i-schwa   0.34905558  0.306223210  0.39188796 0.0000000
## u-schwa   0.87065452  0.827822144  0.91348689 0.0000000
## ae-a     -0.14171414 -0.184546513 -0.09888177 0.0000000
## i-a       0.03434482 -0.008487554  0.07717719 0.1842141
## u-a       0.55594375  0.513111380  0.59877613 0.0000000
## i-ae      0.17605896  0.133226587  0.21889133 0.0000000
## u-ae      0.69765789  0.654825521  0.74049027 0.0000000
## u-i       0.52159893  0.478766562  0.56443131 0.0000000
## 
## Call:
## lm(formula = acoustic.err ~ vowel + VTRatio + I(VTRatio^2) + 
##     (vowel:VTRatio) + (vowel:I(VTRatio^2)) + replication, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.21945 -0.18380 -0.03877  0.14912  1.42829 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           2.596e+01  1.252e+00  20.731  < 2e-16 ***
## vowela                1.305e+01  1.832e+00   7.123 1.32e-12 ***
## vowelae               2.107e+01  2.073e+00  10.162  < 2e-16 ***
## voweli                9.243e+00  1.747e+00   5.292 1.30e-07 ***
## vowelu                4.145e+01  1.770e+00  23.422  < 2e-16 ***
## VTRatio              -1.103e+02  5.552e+00 -19.859  < 2e-16 ***
## I(VTRatio^2)          1.173e+02  6.106e+00  19.217  < 2e-16 ***
## replication           2.419e-05  1.719e-04   0.141    0.888    
## vowela:VTRatio       -5.406e+01  8.110e+00  -6.666 3.12e-11 ***
## vowelae:VTRatio      -8.756e+01  9.122e+00  -9.599  < 2e-16 ***
## voweli:VTRatio       -3.902e+01  7.736e+00  -5.044 4.83e-07 ***
## vowelu:VTRatio       -1.869e+02  7.850e+00 -23.809  < 2e-16 ***
## vowela:I(VTRatio^2)   5.682e+01  8.909e+00   6.377 2.08e-10 ***
## vowelae:I(VTRatio^2)  9.095e+01  9.959e+00   9.132  < 2e-16 ***
## voweli:I(VTRatio^2)   4.247e+01  8.503e+00   4.995 6.21e-07 ***
## vowelu:I(VTRatio^2)   2.130e+02  8.640e+00  24.651  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2718 on 2984 degrees of freedom
## Multiple R-squared:  0.7796, Adjusted R-squared:  0.7785 
## F-statistic: 703.6 on 15 and 2984 DF,  p-value: < 2.2e-16
Summary of Euclidean distance regression (for non-factor DVs and ‘.’ for factors), p-values, and adjusted R2. Interactions are denoted by ‘:’.
DVs, interactions & R2 Euclid.dist
vowel . (0***)
VTRatio -1.1e+02 (1.6e-82***)
VTRatio^2 1.2e+02 (1.1e-77***)
replication 2.4e-05 (0.89)
vowel:VTRatio . (3e-193***)
vowel:VTRatio^2 . (8.6e-135***)
adjusted R2 77.8%

Is VT ratio compensated by other articulators?

##                      Df Sum Sq Mean Sq F value   Pr(>F)    
## VTRatio               1     97    96.6  46.002 1.42e-11 ***
## I(VTRatio^2)          1     90    89.5  42.610 7.82e-11 ***
## vowel                 4   2284   571.0 271.821  < 2e-16 ***
## replication           1      0     0.1   0.068    0.795    
## generation            1    461   461.3 219.587  < 2e-16 ***
## VTRatio:vowel         4    285    71.3  33.953  < 2e-16 ***
## I(VTRatio^2):vowel    4    125    31.2  14.864 4.96e-12 ***
## Residuals          2983   6266     2.1                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = ja.m0)
## 
## $vowel
##                diff        lwr        upr     p adj
## a-schwa  -1.4188451 -1.6472365 -1.1904538 0.0000000
## ae-schwa -2.1863701 -2.4147615 -1.9579787 0.0000000
## i-schwa  -0.6146635 -0.8430549 -0.3862721 0.0000000
## u-schwa   0.1051074 -0.1232840  0.3334988 0.7181736
## ae-a     -0.7675250 -0.9959164 -0.5391336 0.0000000
## i-a       0.8041816  0.5757902  1.0325730 0.0000000
## u-a       1.5239525  1.2955611  1.7523439 0.0000000
## i-ae      1.5717066  1.3433152  1.8000980 0.0000000
## u-ae      2.2914775  2.0630861  2.5198689 0.0000000
## u-i       0.7197709  0.4913795  0.9481623 0.0000000
## 
## Call:
## lm(formula = JA ~ VTRatio + I(VTRatio^2) + vowel + (VTRatio:vowel) + 
##     (I(VTRatio^2):vowel) + replication + generation, data = d)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.9170 -0.8975 -0.0679  0.7434  4.5071 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          -6.972e+01  6.796e+00 -10.259  < 2e-16 ***
## VTRatio               2.802e+02  3.009e+01   9.313  < 2e-16 ***
## I(VTRatio^2)         -2.925e+02  3.308e+01  -8.840  < 2e-16 ***
## vowela                4.056e+01  9.786e+00   4.145 3.49e-05 ***
## vowelae               3.807e+01  1.106e+01   3.443 0.000582 ***
## voweli                6.365e+01  9.356e+00   6.803 1.24e-11 ***
## vowelu                7.474e+01  9.607e+00   7.779 9.99e-15 ***
## replication           3.096e-05  9.170e-04   0.034 0.973069    
## generation           -3.196e-03  2.803e-04 -11.401  < 2e-16 ***
## VTRatio:vowela       -1.770e+02  4.332e+01  -4.085 4.52e-05 ***
## VTRatio:vowelae      -1.727e+02  4.864e+01  -3.550 0.000391 ***
## VTRatio:voweli       -2.797e+02  4.145e+01  -6.748 1.79e-11 ***
## VTRatio:vowelu       -3.092e+02  4.259e+01  -7.261 4.89e-13 ***
## I(VTRatio^2):vowela   1.849e+02  4.758e+01   3.886 0.000104 ***
## I(VTRatio^2):vowelae  1.827e+02  5.311e+01   3.440 0.000589 ***
## I(VTRatio^2):voweli   3.013e+02  4.556e+01   6.613 4.45e-11 ***
## I(VTRatio^2):vowelu   3.166e+02  4.683e+01   6.761 1.64e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.449 on 2983 degrees of freedom
## Multiple R-squared:  0.3478, Adjusted R-squared:  0.3443 
## F-statistic: 99.43 on 16 and 2983 DF,  p-value: < 2.2e-16
##                      Df Sum Sq Mean Sq F value   Pr(>F)    
## VTRatio               1   85.8   85.80 465.210  < 2e-16 ***
## I(VTRatio^2)          1    0.7    0.75   4.053 0.044193 *  
## vowel                 4  358.3   89.58 485.655  < 2e-16 ***
## replication           1    0.1    0.11   0.617 0.432078    
## generation            1    6.9    6.90  37.394 1.09e-09 ***
## VTRatio:vowel         4   45.6   11.40  61.801  < 2e-16 ***
## I(VTRatio^2):vowel    4    4.1    1.03   5.606 0.000171 ***
## Residuals          2983  550.2    0.18                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = lp.m0)
## 
## $vowel
##                 diff          lwr         upr    p adj
## a-schwa  -0.14674552 -0.214422890 -0.07906815 0.000000
## ae-schwa -0.43553221 -0.503209585 -0.36785484 0.000000
## i-schwa   0.06157664 -0.006100734  0.12925401 0.094632
## u-schwa   0.61863029  0.550952917  0.68630766 0.000000
## ae-a     -0.28878670 -0.356464067 -0.22110932 0.000000
## i-a       0.20832216  0.140644785  0.27599953 0.000000
## u-a       0.76537581  0.697698435  0.83305318 0.000000
## i-ae      0.49710885  0.429431480  0.56478622 0.000000
## u-ae      1.05416250  0.986485130  1.12183987 0.000000
## u-i       0.55705365  0.489376279  0.62473102 0.000000
## 
## Call:
## lm(formula = LP ~ VTRatio + I(VTRatio^2) + vowel + (VTRatio:vowel) + 
##     (I(VTRatio^2):vowel) + replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.80886 -0.22899  0.07017  0.28533  1.44607 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          -1.229e+01  2.014e+00  -6.102 1.18e-09 ***
## VTRatio               4.735e+01  8.916e+00   5.310 1.18e-07 ***
## I(VTRatio^2)         -4.474e+01  9.803e+00  -4.564 5.23e-06 ***
## vowela                1.307e+01  2.900e+00   4.509 6.77e-06 ***
## vowelae               3.815e+00  3.276e+00   1.165 0.244252    
## voweli                7.605e+00  2.772e+00   2.743 0.006127 ** 
## vowelu                9.395e+00  2.847e+00   3.300 0.000978 ***
## replication          -1.494e-04  2.717e-04  -0.550 0.582453    
## generation            7.567e-04  8.307e-05   9.110  < 2e-16 ***
## VTRatio:vowela       -5.699e+01  1.284e+01  -4.439 9.37e-06 ***
## VTRatio:vowelae      -1.242e+01  1.441e+01  -0.862 0.388934    
## VTRatio:voweli       -3.393e+01  1.228e+01  -2.763 0.005767 ** 
## VTRatio:vowelu       -3.334e+01  1.262e+01  -2.641 0.008299 ** 
## I(VTRatio^2):vowela   6.063e+01  1.410e+01   4.300 1.76e-05 ***
## I(VTRatio^2):vowelae  6.738e+00  1.574e+01   0.428 0.668591    
## I(VTRatio^2):voweli   3.782e+01  1.350e+01   2.801 0.005125 ** 
## I(VTRatio^2):vowelu   3.024e+01  1.388e+01   2.179 0.029374 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4295 on 2983 degrees of freedom
## Multiple R-squared:  0.4769, Adjusted R-squared:  0.4741 
## F-statistic:   170 on 16 and 2983 DF,  p-value: < 2.2e-16
##                      Df Sum Sq Mean Sq F value Pr(>F)    
## VTRatio               1  212.6   212.6 292.485 <2e-16 ***
## I(VTRatio^2)          1    0.1     0.1   0.131  0.717    
## vowel                 4 1748.7   437.2 601.394 <2e-16 ***
## replication           1    0.6     0.6   0.851  0.356    
## generation            1    1.7     1.7   2.369  0.124    
## VTRatio:vowel         4  148.0    37.0  50.895 <2e-16 ***
## I(VTRatio^2):vowel    4    8.6     2.1   2.951  0.019 *  
## Residuals          2983 2168.5     0.7                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = ld.m0)
## 
## $vowel
##                diff        lwr         upr     p adj
## a-schwa   0.4250860  0.2907280  0.55944391 0.0000000
## ae-schwa  0.6692683  0.5349103  0.80362619 0.0000000
## i-schwa  -0.2096318 -0.3439898 -0.07527389 0.0002057
## u-schwa  -1.5224091 -1.6567671 -1.38805120 0.0000000
## ae-a      0.2441823  0.1098243  0.37854021 0.0000074
## i-a      -0.6347178 -0.7690757 -0.50035987 0.0000000
## u-a      -1.9474951 -2.0818530 -1.81313718 0.0000000
## i-ae     -0.8789001 -1.0132580 -0.74454214 0.0000000
## u-ae     -2.1916774 -2.3260353 -2.05731945 0.0000000
## u-i      -1.3127773 -1.4471352 -1.17841938 0.0000000
## 
## Call:
## lm(formula = LD ~ VTRatio + I(VTRatio^2) + vowel + (VTRatio:vowel) + 
##     (I(VTRatio^2):vowel) + replication + generation, data = d)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.1135 -0.4766 -0.1655  0.4680  3.3911 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)   
## (Intercept)           1.227e+01  3.998e+00   3.068  0.00217 **
## VTRatio              -3.373e+01  1.770e+01  -1.905  0.05683 . 
## I(VTRatio^2)          2.373e+01  1.946e+01   1.219  0.22275   
## vowela               -1.544e+01  5.757e+00  -2.681  0.00737 **
## vowelae               6.677e-01  6.503e+00   0.103  0.91824   
## voweli               -8.820e+00  5.504e+00  -1.603  0.10915   
## vowelu               -6.712e+00  5.652e+00  -1.188  0.23506   
## replication          -5.239e-04  5.394e-04  -0.971  0.33149   
## generation           -2.323e-04  1.649e-04  -1.409  0.15905   
## VTRatio:vowela        6.461e+01  2.549e+01   2.535  0.01130 * 
## VTRatio:vowelae      -1.203e+01  2.861e+01  -0.421  0.67412   
## VTRatio:voweli        3.880e+01  2.438e+01   1.591  0.11168   
## VTRatio:vowelu        1.270e+01  2.505e+01   0.507  0.61239   
## I(VTRatio^2):vowela  -6.466e+01  2.799e+01  -2.310  0.02094 * 
## I(VTRatio^2):vowelae  2.627e+01  3.124e+01   0.841  0.40056   
## I(VTRatio^2):voweli  -4.332e+01  2.680e+01  -1.616  0.10611   
## I(VTRatio^2):vowelu  -2.561e+00  2.755e+01  -0.093  0.92595   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8526 on 2983 degrees of freedom
## Multiple R-squared:  0.4944, Adjusted R-squared:  0.4917 
## F-statistic: 182.3 on 16 and 2983 DF,  p-value: < 2.2e-16
##                      Df Sum Sq Mean Sq F value   Pr(>F)    
## VTRatio               1     16    16.0   83.48  < 2e-16 ***
## I(VTRatio^2)          1    255   255.3 1335.10  < 2e-16 ***
## vowel                 4   3801   950.3 4969.98  < 2e-16 ***
## replication           1      0     0.2    1.05    0.306    
## generation            1      8     7.9   41.21 1.59e-10 ***
## VTRatio:vowel         4    472   118.0  617.05  < 2e-16 ***
## I(VTRatio^2):vowel    4    289    72.2  377.72  < 2e-16 ***
## Residuals          2983    570     0.2                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = tcx.m0)
## 
## $vowel
##                diff        lwr         upr    p adj
## a-schwa  -0.3015031 -0.3704093 -0.23259689 0.00e+00
## ae-schwa  1.2917062  1.2228000  1.36061243 0.00e+00
## i-schwa   2.6520663  2.5831600  2.72097248 0.00e+00
## u-schwa  -0.1226092 -0.1915154 -0.05370297 1.24e-05
## ae-a      1.5932093  1.5243031  1.66211553 0.00e+00
## i-a       2.9535694  2.8846631  3.02247559 0.00e+00
## u-a       0.1788939  0.1099877  0.24780014 0.00e+00
## i-ae      1.3603601  1.2914538  1.42926628 0.00e+00
## u-ae     -1.4143154 -1.4832216 -1.34540918 0.00e+00
## u-i      -2.7746755 -2.8435817 -2.70576923 0.00e+00
## 
## Call:
## lm(formula = TCX ~ VTRatio + I(VTRatio^2) + vowel + (VTRatio:vowel) + 
##     (I(VTRatio^2):vowel) + replication + generation, data = d)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.3860 -0.1648 -0.0227  0.1489  3.2585 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          -1.326e+01  2.050e+00  -6.468 1.15e-10 ***
## VTRatio               5.575e+01  9.078e+00   6.141 9.27e-10 ***
## I(VTRatio^2)         -5.975e+01  9.981e+00  -5.987 2.40e-09 ***
## vowela                5.347e+00  2.952e+00   1.811  0.07023 .  
## vowelae               8.735e+00  3.335e+00   2.619  0.00886 ** 
## voweli               -8.257e+01  2.823e+00 -29.251  < 2e-16 ***
## vowelu                1.339e+01  2.899e+00   4.621 3.98e-06 ***
## replication           2.972e-04  2.766e-04   1.074  0.28286    
## generation           -4.715e-05  8.457e-05  -0.558  0.57722    
## VTRatio:vowela       -2.457e+01  1.307e+01  -1.880  0.06020 .  
## VTRatio:vowelae      -1.557e+01  1.467e+01  -1.061  0.28876    
## VTRatio:voweli        3.659e+02  1.250e+01  29.263  < 2e-16 ***
## VTRatio:vowelu       -6.513e+01  1.285e+01  -5.069 4.24e-07 ***
## I(VTRatio^2):vowela   2.653e+01  1.435e+01   1.848  0.06465 .  
## I(VTRatio^2):vowelae -1.531e+00  1.602e+01  -0.096  0.92389    
## I(VTRatio^2):voweli  -3.887e+02  1.375e+01 -28.279  < 2e-16 ***
## I(VTRatio^2):vowelu   7.736e+01  1.413e+01   5.476 4.72e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4373 on 2983 degrees of freedom
## Multiple R-squared:  0.8946, Adjusted R-squared:  0.894 
## F-statistic:  1582 on 16 and 2983 DF,  p-value: < 2.2e-16
##                      Df Sum Sq Mean Sq  F value   Pr(>F)    
## VTRatio               1  239.7  239.66 2157.597  < 2e-16 ***
## I(VTRatio^2)          1    7.2    7.25   65.241 9.52e-16 ***
## vowel                 4  775.2  193.79 1744.632  < 2e-16 ***
## replication           1    0.0    0.05    0.409    0.522    
## generation            1    2.2    2.16   19.452 1.07e-05 ***
## VTRatio:vowel         4  142.7   35.68  321.190  < 2e-16 ***
## I(VTRatio^2):vowel    4   33.3    8.32   74.869  < 2e-16 ***
## Residuals          2983  331.3    0.11                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = tcy.m0)
## 
## $vowel
##                 diff         lwr        upr     p adj
## a-schwa  -0.35923000 -0.41175066 -0.3067093 0.0000000
## ae-schwa -0.28160479 -0.33412545 -0.2290841 0.0000000
## i-schwa   0.99696196  0.94444130  1.0494826 0.0000000
## u-schwa   0.47650375  0.42398309  0.5290244 0.0000000
## ae-a      0.07762521  0.02510455  0.1301459 0.0005381
## i-a       1.35619196  1.30367130  1.4087126 0.0000000
## u-a       0.83573375  0.78321309  0.8882544 0.0000000
## i-ae      1.27856675  1.22604609  1.3310874 0.0000000
## u-ae      0.75810854  0.70558788  0.8106292 0.0000000
## u-i      -0.52045821 -0.57297886 -0.4679376 0.0000000
## 
## Call:
## lm(formula = TCY ~ VTRatio + I(VTRatio^2) + vowel + (VTRatio:vowel) + 
##     (I(VTRatio^2):vowel) + replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.60082 -0.11231  0.02532  0.17679  0.85886 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          -2.556e+01  1.563e+00 -16.355  < 2e-16 ***
## VTRatio               9.492e+01  6.919e+00  13.719  < 2e-16 ***
## I(VTRatio^2)         -9.362e+01  7.607e+00 -12.306  < 2e-16 ***
## vowela                2.394e+01  2.250e+00  10.637  < 2e-16 ***
## vowelae               3.393e+01  2.542e+00  13.346  < 2e-16 ***
## voweli                7.531e+00  2.152e+00   3.500 0.000471 ***
## vowelu                1.645e+01  2.209e+00   7.448 1.23e-13 ***
## replication           1.657e-04  2.109e-04   0.786 0.431971    
## generation           -1.822e-06  6.446e-05  -0.028 0.977454    
## VTRatio:vowela       -1.104e+02  9.963e+00 -11.082  < 2e-16 ***
## VTRatio:vowelae      -1.499e+02  1.119e+01 -13.405  < 2e-16 ***
## VTRatio:voweli       -1.703e+01  9.531e+00  -1.787 0.074018 .  
## VTRatio:vowelu       -6.634e+01  9.794e+00  -6.773 1.51e-11 ***
## I(VTRatio^2):vowela   1.241e+02  1.094e+01  11.344  < 2e-16 ***
## I(VTRatio^2):vowelae  1.628e+02  1.221e+01  13.328  < 2e-16 ***
## I(VTRatio^2):voweli   5.595e+00  1.048e+01   0.534 0.593386    
## I(VTRatio^2):vowelu   6.788e+01  1.077e+01   6.304 3.34e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3333 on 2983 degrees of freedom
## Multiple R-squared:  0.7837, Adjusted R-squared:  0.7825 
## F-statistic: 675.3 on 16 and 2983 DF,  p-value: < 2.2e-16
##                      Df Sum Sq Mean Sq F value   Pr(>F)    
## VTRatio               1   69.7   69.72 106.683  < 2e-16 ***
## I(VTRatio^2)          1   30.6   30.64  46.886 9.10e-12 ***
## vowel                 4  206.0   51.51  78.828  < 2e-16 ***
## replication           1    0.1    0.10   0.158  0.69060    
## generation            1    6.1    6.11   9.354  0.00225 ** 
## VTRatio:vowel         4   51.8   12.94  19.803 4.18e-16 ***
## I(VTRatio^2):vowel    4   81.4   20.36  31.150  < 2e-16 ***
## Residuals          2983 1949.3    0.65                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = ttx.m0)
## 
## $vowel
##                 diff         lwr         upr     p adj
## a-schwa  -0.22458537 -0.35197355 -0.09719720 0.0000155
## ae-schwa -0.29881731 -0.42620549 -0.17142913 0.0000000
## i-schwa  -0.05597787 -0.18336605  0.07141031 0.7517734
## u-schwa  -0.74089991 -0.86828809 -0.61351173 0.0000000
## ae-a     -0.07423193 -0.20162011  0.05315625 0.5035769
## i-a       0.16860750  0.04121932  0.29599568 0.0028463
## u-a      -0.51631454 -0.64370272 -0.38892636 0.0000000
## i-ae      0.24283944  0.11545126  0.37022761 0.0000021
## u-ae     -0.44208260 -0.56947078 -0.31469442 0.0000000
## u-i      -0.68492204 -0.81231022 -0.55753386 0.0000000
## 
## Call:
## lm(formula = TTX ~ VTRatio + I(VTRatio^2) + vowel + (VTRatio:vowel) + 
##     (I(VTRatio^2):vowel) + replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.54546 -0.56528  0.02582  0.48628  2.88167 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           2.629e+01  3.791e+00   6.936 4.93e-12 ***
## VTRatio              -9.485e+01  1.678e+01  -5.652 1.74e-08 ***
## I(VTRatio^2)          9.743e+01  1.845e+01   5.280 1.38e-07 ***
## vowela                1.810e+01  5.458e+00   3.316 0.000925 ***
## vowelae              -6.798e+00  6.166e+00  -1.102 0.270360    
## voweli               -4.296e+01  5.219e+00  -8.232 2.73e-16 ***
## vowelu               -7.295e+00  5.359e+00  -1.361 0.173498    
## replication          -2.399e-04  5.114e-04  -0.469 0.639025    
## generation           -4.208e-04  1.564e-04  -2.691 0.007154 ** 
## VTRatio:vowela       -8.144e+01  2.416e+01  -3.370 0.000761 ***
## VTRatio:vowelae       2.731e+01  2.713e+01   1.007 0.314230    
## VTRatio:voweli        1.823e+02  2.312e+01   7.884 4.42e-15 ***
## VTRatio:vowelu        2.558e+01  2.375e+01   1.077 0.281554    
## I(VTRatio^2):vowela   8.974e+01  2.654e+01   3.381 0.000730 ***
## I(VTRatio^2):vowelae -2.835e+01  2.962e+01  -0.957 0.338549    
## I(VTRatio^2):voweli  -1.914e+02  2.541e+01  -7.534 6.50e-14 ***
## I(VTRatio^2):vowelu  -2.415e+01  2.612e+01  -0.925 0.355231    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8084 on 2983 degrees of freedom
## Multiple R-squared:  0.1861, Adjusted R-squared:  0.1818 
## F-statistic: 42.64 on 16 and 2983 DF,  p-value: < 2.2e-16
##                      Df Sum Sq Mean Sq F value   Pr(>F)    
## VTRatio               1  540.8   540.8  906.29  < 2e-16 ***
## I(VTRatio^2)          1  285.1   285.1  477.79  < 2e-16 ***
## vowel                 4  211.9    53.0   88.79  < 2e-16 ***
## replication           1    0.1     0.1    0.22    0.639    
## generation            1   39.0    39.0   65.43 8.66e-16 ***
## VTRatio:vowel         4  200.3    50.1   83.90  < 2e-16 ***
## I(VTRatio^2):vowel    4   53.9    13.5   22.57  < 2e-16 ***
## Residuals          2983 1780.0     0.6                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = tty.m0)
## 
## $vowel
##                 diff         lwr        upr     p adj
## a-schwa  -0.29837990 -0.42011074 -0.1766491 0.0000000
## ae-schwa -0.32031634 -0.44204717 -0.1985855 0.0000000
## i-schwa   0.05813804 -0.06359279  0.1798689 0.6890293
## u-schwa   0.40309833  0.28136749  0.5248292 0.0000000
## ae-a     -0.02193643 -0.14366727  0.0997944 0.9881375
## i-a       0.35651795  0.23478711  0.4782488 0.0000000
## u-a       0.70147823  0.57974739  0.8232091 0.0000000
## i-ae      0.37845438  0.25672355  0.5001852 0.0000000
## u-ae      0.72341466  0.60168383  0.8451455 0.0000000
## u-i       0.34496028  0.22322945  0.4666911 0.0000000
## 
## Call:
## lm(formula = TTY ~ VTRatio + I(VTRatio^2) + vowel + (VTRatio:vowel) + 
##     (I(VTRatio^2):vowel) + replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.93819 -0.49788  0.06723  0.58266  2.02239 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           3.451e+01  3.622e+00   9.528  < 2e-16 ***
## VTRatio              -1.696e+02  1.604e+01 -10.577  < 2e-16 ***
## I(VTRatio^2)          1.988e+02  1.763e+01  11.273  < 2e-16 ***
## vowela               -7.054e+00  5.216e+00  -1.352 0.176333    
## vowelae               2.188e+00  5.892e+00   0.371 0.710375    
## voweli                1.171e+01  4.987e+00   2.349 0.018904 *  
## vowelu               -3.611e+01  5.121e+00  -7.052 2.19e-12 ***
## replication          -1.848e-04  4.887e-04  -0.378 0.705404    
## generation            5.037e-04  1.494e-04   3.371 0.000758 ***
## VTRatio:vowela        2.827e+01  2.309e+01   1.224 0.221029    
## VTRatio:vowelae      -1.487e+01  2.592e+01  -0.574 0.566261    
## VTRatio:voweli       -3.824e+01  2.209e+01  -1.731 0.083538 .  
## VTRatio:vowelu        1.624e+02  2.270e+01   7.154 1.06e-12 ***
## I(VTRatio^2):vowela  -2.928e+01  2.536e+01  -1.155 0.248275    
## I(VTRatio^2):vowelae  2.046e+01  2.831e+01   0.723 0.469963    
## I(VTRatio^2):voweli   2.732e+01  2.428e+01   1.125 0.260598    
## I(VTRatio^2):vowelu  -1.790e+02  2.496e+01  -7.171 9.34e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7725 on 2983 degrees of freedom
## Multiple R-squared:  0.4279, Adjusted R-squared:  0.4248 
## F-statistic: 139.4 on 16 and 2983 DF,  p-value: < 2.2e-16
##                      Df Sum Sq Mean Sq F value   Pr(>F)    
## VTRatio               1      1    1.49   1.214 0.270691    
## I(VTRatio^2)          1      0    0.37   0.298 0.585195    
## vowel                 4    950  237.44 193.783  < 2e-16 ***
## replication           1      0    0.30   0.247 0.619006    
## generation            1     16   15.81  12.902 0.000333 ***
## VTRatio:vowel         4    241   60.25  49.174  < 2e-16 ***
## I(VTRatio^2):vowel    4     80   19.98  16.306 3.21e-13 ***
## Residuals          2983   3655    1.23                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = tbx.m0)
## 
## $vowel
##                diff        lwr         upr     p adj
## a-schwa  -0.2457704 -0.4202039 -0.07133692 0.0011593
## ae-schwa  0.4448208  0.2703873  0.61925428 0.0000000
## i-schwa   1.0271992  0.8527657  1.20163266 0.0000000
## u-schwa  -0.5909198 -0.7653533 -0.41648633 0.0000000
## ae-a      0.6905912  0.5161577  0.86502469 0.0000000
## i-a       1.2729696  1.0985361  1.44740308 0.0000000
## u-a      -0.3451494 -0.5195829 -0.17071592 0.0000007
## i-ae      0.5823784  0.4079449  0.75681188 0.0000000
## u-ae     -1.0357406 -1.2101741 -0.86130712 0.0000000
## u-i      -1.6181190 -1.7925525 -1.44368551 0.0000000
## 
## Call:
## lm(formula = TBX ~ VTRatio + I(VTRatio^2) + vowel + (VTRatio:vowel) + 
##     (I(VTRatio^2):vowel) + replication + generation, data = d)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.7123 -0.7413 -0.0707  0.7779  3.2861 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           2.012e+01  5.191e+00   3.876 0.000109 ***
## VTRatio              -7.826e+01  2.298e+01  -3.406 0.000669 ***
## I(VTRatio^2)          7.950e+01  2.527e+01   3.146 0.001669 ** 
## vowela               -4.917e+00  7.474e+00  -0.658 0.510688    
## vowelae              -5.370e-01  8.443e+00  -0.064 0.949291    
## voweli               -5.187e+01  7.146e+00  -7.259 4.96e-13 ***
## vowelu               -1.251e+01  7.338e+00  -1.705 0.088226 .  
## replication          -2.975e-04  7.003e-04  -0.425 0.671042    
## generation            6.885e-04  2.141e-04   3.216 0.001314 ** 
## VTRatio:vowela        7.520e+00  3.309e+01   0.227 0.820242    
## VTRatio:vowelae       8.437e+00  3.715e+01   0.227 0.820344    
## VTRatio:voweli        2.228e+02  3.165e+01   7.037 2.43e-12 ***
## VTRatio:vowelu        4.435e+01  3.253e+01   1.363 0.172869    
## I(VTRatio^2):vowela   6.002e+00  3.634e+01   0.165 0.868814    
## I(VTRatio^2):vowelae -1.341e+01  4.056e+01  -0.331 0.740912    
## I(VTRatio^2):voweli  -2.317e+02  3.480e+01  -6.659 3.27e-11 ***
## I(VTRatio^2):vowelu  -3.956e+01  3.576e+01  -1.106 0.268819    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.107 on 2983 degrees of freedom
## Multiple R-squared:  0.2607, Adjusted R-squared:  0.2567 
## F-statistic: 65.73 on 16 and 2983 DF,  p-value: < 2.2e-16
##                      Df Sum Sq Mean Sq F value   Pr(>F)    
## VTRatio               1   50.8    50.8   97.02  < 2e-16 ***
## I(VTRatio^2)          1    0.1     0.1    0.10 0.751494    
## vowel                 4 1784.1   446.0  851.23  < 2e-16 ***
## replication           1    0.0     0.0    0.00 0.999265    
## generation            1    6.3     6.3   12.06 0.000522 ***
## VTRatio:vowel         4   77.2    19.3   36.85  < 2e-16 ***
## I(VTRatio^2):vowel    4   61.5    15.4   29.34  < 2e-16 ***
## Residuals          2983 1563.1     0.5                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = tby.m0)
## 
## $vowel
##                 diff        lwr         upr     p adj
## a-schwa  -1.29123003 -1.4053011 -1.17715898 0.0000000
## ae-schwa -0.42475277 -0.5388238 -0.31068172 0.0000000
## i-schwa   1.10212114  0.9880501  1.21619219 0.0000000
## u-schwa  -0.07764574 -0.1917168  0.03642531 0.3405815
## ae-a      0.86647725  0.7524062  0.98054831 0.0000000
## i-a       2.39335117  2.2792801  2.50742222 0.0000000
## u-a       1.21358429  1.0995132  1.32765534 0.0000000
## i-ae      1.52687391  1.4128029  1.64094497 0.0000000
## u-ae      0.34710704  0.2330360  0.46117809 0.0000000
## u-i      -1.17976688 -1.2938379 -1.06569583 0.0000000
## 
## Call:
## lm(formula = TBY ~ VTRatio + I(VTRatio^2) + vowel + (VTRatio:vowel) + 
##     (I(VTRatio^2):vowel) + replication + generation, data = d)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.8343 -0.4214  0.1032  0.4856  2.0213 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           3.000e+01  3.394e+00   8.839  < 2e-16 ***
## VTRatio              -1.324e+02  1.503e+01  -8.808  < 2e-16 ***
## I(VTRatio^2)          1.466e+02  1.652e+01   8.872  < 2e-16 ***
## vowela               -4.403e+01  4.888e+00  -9.009  < 2e-16 ***
## vowelae              -3.057e+01  5.521e+00  -5.537 3.34e-08 ***
## voweli               -4.339e+01  4.673e+00  -9.286  < 2e-16 ***
## vowelu               -3.816e+01  4.798e+00  -7.953 2.57e-15 ***
## replication          -1.380e-05  4.580e-04  -0.030    0.976    
## generation            8.545e-06  1.400e-04   0.061    0.951    
## VTRatio:vowela        1.894e+02  2.164e+01   8.754  < 2e-16 ***
## VTRatio:vowelae       1.274e+02  2.429e+01   5.243 1.69e-07 ***
## VTRatio:voweli        1.996e+02  2.070e+01   9.644  < 2e-16 ***
## VTRatio:vowelu        1.618e+02  2.127e+01   7.604 3.81e-14 ***
## I(VTRatio^2):vowela  -2.079e+02  2.376e+01  -8.747  < 2e-16 ***
## I(VTRatio^2):vowelae -1.330e+02  2.653e+01  -5.012 5.70e-07 ***
## I(VTRatio^2):voweli  -2.217e+02  2.276e+01  -9.744  < 2e-16 ***
## I(VTRatio^2):vowelu  -1.697e+02  2.339e+01  -7.257 5.01e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7239 on 2983 degrees of freedom
## Multiple R-squared:  0.5589, Adjusted R-squared:  0.5565 
## F-statistic: 236.2 on 16 and 2983 DF,  p-value: < 2.2e-16
##                      Df Sum Sq Mean Sq F value   Pr(>F)    
## VTRatio               1   5.14    5.14 109.899  < 2e-16 ***
## I(VTRatio^2)          1   8.81    8.81 188.169  < 2e-16 ***
## vowel                 4 167.56   41.89 895.065  < 2e-16 ***
## replication           1   0.04    0.04   0.943    0.332    
## generation            1   1.99    1.99  42.618 7.79e-11 ***
## VTRatio:vowel         4  33.03    8.26 176.462  < 2e-16 ***
## I(VTRatio^2):vowel    4   1.56    0.39   8.353 1.07e-06 ***
## Residuals          2983 139.60    0.05                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = hx.m0)
## 
## $vowel
##                 diff         lwr         upr     p adj
## a-schwa  -0.29974587 -0.33383668 -0.26565507 0.0000000
## ae-schwa -0.21643711 -0.25052792 -0.18234631 0.0000000
## i-schwa   0.28933473  0.25524393  0.32342554 0.0000000
## u-schwa   0.24194638  0.20785557  0.27603718 0.0000000
## ae-a      0.08330876  0.04921796  0.11739956 0.0000000
## i-a       0.58908061  0.55498980  0.62317141 0.0000000
## u-a       0.54169225  0.50760145  0.57578305 0.0000000
## i-ae      0.50577185  0.47168104  0.53986265 0.0000000
## u-ae      0.45838349  0.42429269  0.49247429 0.0000000
## u-i      -0.04738836 -0.08147916 -0.01329755 0.0014212
## 
## Call:
## lm(formula = HX ~ VTRatio + I(VTRatio^2) + vowel + (VTRatio:vowel) + 
##     (I(VTRatio^2):vowel) + replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.74661 -0.11349 -0.01116  0.12197  0.88658 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          -9.501e+00  1.014e+00  -9.366  < 2e-16 ***
## VTRatio               4.297e+01  4.491e+00   9.568  < 2e-16 ***
## I(VTRatio^2)         -4.582e+01  4.938e+00  -9.279  < 2e-16 ***
## vowela                5.956e+00  1.461e+00   4.077 4.67e-05 ***
## vowelae              -8.549e-01  1.650e+00  -0.518 0.604429    
## voweli                7.888e+00  1.397e+00   5.648 1.77e-08 ***
## vowelu                5.931e+00  1.434e+00   4.136 3.63e-05 ***
## replication          -1.567e-04  1.369e-04  -1.145 0.252284    
## generation           -3.298e-04  4.184e-05  -7.881 4.51e-15 ***
## VTRatio:vowela       -2.798e+01  6.467e+00  -4.327 1.56e-05 ***
## VTRatio:vowelae       3.602e+00  7.260e+00   0.496 0.619862    
## VTRatio:voweli       -2.747e+01  6.186e+00  -4.440 9.33e-06 ***
## VTRatio:vowelu       -2.229e+01  6.357e+00  -3.507 0.000460 ***
## I(VTRatio^2):vowela   3.106e+01  7.102e+00   4.373 1.27e-05 ***
## I(VTRatio^2):vowelae -4.876e+00  7.927e+00  -0.615 0.538546    
## I(VTRatio^2):voweli   2.334e+01  6.801e+00   3.432 0.000608 ***
## I(VTRatio^2):vowelu   2.137e+01  6.990e+00   3.057 0.002253 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2163 on 2983 degrees of freedom
## Multiple R-squared:  0.6098, Adjusted R-squared:  0.6077 
## F-statistic: 291.3 on 16 and 2983 DF,  p-value: < 2.2e-16
##                      Df Sum Sq Mean Sq   F value Pr(>F)    
## VTRatio               1  952.7   952.7 51187.014 <2e-16 ***
## I(VTRatio^2)          1   26.8    26.8  1439.735 <2e-16 ***
## vowel                 4    6.5     1.6    87.404 <2e-16 ***
## replication           1    0.0     0.0     0.062 0.8031    
## generation            1    0.1     0.1     6.501 0.0108 *  
## VTRatio:vowel         4    2.3     0.6    30.755 <2e-16 ***
## I(VTRatio^2):vowel    4    2.0     0.5    26.679 <2e-16 ***
## Residuals          2983   55.5     0.0                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = hy.m0)
## 
## $vowel
##                  diff         lwr          upr     p adj
## a-schwa   0.001891314 -0.01960701  0.023389639 0.9992663
## ae-schwa  0.066022343  0.04452402  0.087520668 0.0000000
## i-schwa  -0.031281336 -0.05277966 -0.009783011 0.0006972
## u-schwa  -0.076075012 -0.09757334 -0.054576687 0.0000000
## ae-a      0.064131029  0.04263270  0.085629354 0.0000000
## i-a      -0.033172650 -0.05467097 -0.011674325 0.0002526
## u-a      -0.077966326 -0.09946465 -0.056468001 0.0000000
## i-ae     -0.097303679 -0.11880200 -0.075805354 0.0000000
## u-ae     -0.142097355 -0.16359568 -0.120599030 0.0000000
## u-i      -0.044793676 -0.06629200 -0.023295351 0.0000001
## 
## Call:
## lm(formula = HY ~ VTRatio + I(VTRatio^2) + vowel + (VTRatio:vowel) + 
##     (I(VTRatio^2):vowel) + replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.53399 -0.10757  0.00335  0.09809  0.35259 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          -2.541e+01  6.397e-01 -39.724  < 2e-16 ***
## VTRatio               7.866e+01  2.832e+00  27.774  < 2e-16 ***
## I(VTRatio^2)         -7.140e+01  3.114e+00 -22.930  < 2e-16 ***
## vowela                2.613e+00  9.211e-01   2.836  0.00459 ** 
## vowelae               1.109e+01  1.041e+00  10.657  < 2e-16 ***
## voweli                4.914e+00  8.807e-01   5.579 2.63e-08 ***
## vowelu                5.577e+00  9.043e-01   6.167 7.89e-10 ***
## replication           2.834e-05  8.631e-05   0.328  0.74266    
## generation           -2.825e-05  2.639e-05  -1.070  0.28450    
## VTRatio:vowela       -1.102e+01  4.078e+00  -2.701  0.00695 ** 
## VTRatio:vowelae      -4.664e+01  4.578e+00 -10.187  < 2e-16 ***
## VTRatio:voweli       -2.104e+01  3.901e+00  -5.394 7.42e-08 ***
## VTRatio:vowelu       -2.435e+01  4.009e+00  -6.074 1.41e-09 ***
## I(VTRatio^2):vowela   1.148e+01  4.479e+00   2.564  0.01040 *  
## I(VTRatio^2):vowelae  4.881e+01  4.999e+00   9.763  < 2e-16 ***
## I(VTRatio^2):voweli   2.214e+01  4.289e+00   5.163 2.60e-07 ***
## I(VTRatio^2):vowelu   2.596e+01  4.408e+00   5.889 4.32e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1364 on 2983 degrees of freedom
## Multiple R-squared:  0.9469, Adjusted R-squared:  0.9466 
## F-statistic:  3326 on 16 and 2983 DF,  p-value: < 2.2e-16
##                      Df Sum Sq Mean Sq   F value Pr(>F)    
## VTRatio               1   6.20    6.20  1797.245 <2e-16 ***
## I(VTRatio^2)          1  19.74   19.74  5718.827 <2e-16 ***
## vowel                 4  28.08    7.02  2034.602 <2e-16 ***
## LEN                   1 240.79  240.79 69777.541 <2e-16 ***
## replication           1   0.00    0.00     0.018  0.893    
## generation            1   0.40    0.40   115.819 <2e-16 ***
## VTRatio:vowel         4   1.08    0.27    78.196 <2e-16 ***
## I(VTRatio^2):vowel    4   0.82    0.20    59.056 <2e-16 ***
## Residuals          2982  10.29    0.00                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = hy_norm.m0)
## 
## $vowel
##                 diff         lwr          upr     p adj
## a-schwa  -0.00966916 -0.01892635 -0.000411967 0.0355306
## ae-schwa  0.10506210  0.09580491  0.114319296 0.0000000
## i-schwa  -0.08902487 -0.09828206 -0.079767678 0.0000000
## u-schwa  -0.18432645 -0.19358364 -0.175069258 0.0000000
## ae-a      0.11473126  0.10547407  0.123988456 0.0000000
## i-a      -0.07935571 -0.08861290 -0.070098518 0.0000000
## u-a      -0.17465729 -0.18391448 -0.165400098 0.0000000
## i-ae     -0.19408697 -0.20334417 -0.184829781 0.0000000
## u-ae     -0.28938855 -0.29864575 -0.280131361 0.0000000
## u-i      -0.09530158 -0.10455877 -0.086044388 0.0000000
## 
## Call:
## lm(formula = HY_norm ~ VTRatio + I(VTRatio^2) + vowel + LEN + 
##     (VTRatio:vowel) + (I(VTRatio^2):vowel) + replication + generation, 
##     data = d)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.172669 -0.033536  0.003652  0.034660  0.283161 
## 
## Coefficients:
##                        Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)          -5.624e+01  3.177e-01 -177.007  < 2e-16 ***
## VTRatio               1.323e+02  1.243e+00  106.454  < 2e-16 ***
## I(VTRatio^2)         -9.408e+01  1.343e+00  -70.074  < 2e-16 ***
## vowela               -1.414e+00  3.971e-01   -3.560 0.000377 ***
## vowelae              -6.232e+00  4.558e-01  -13.674  < 2e-16 ***
## voweli                7.610e-01  3.811e-01    1.997 0.045923 *  
## vowelu               -2.768e-01  3.920e-01   -0.706 0.480220    
## LEN                  -2.059e+00  7.972e-03 -258.282  < 2e-16 ***
## replication          -9.179e-06  3.717e-05   -0.247 0.804954    
## generation           -1.133e-04  1.136e-05   -9.966  < 2e-16 ***
## VTRatio:vowela        6.101e+00  1.758e+00    3.470 0.000527 ***
## VTRatio:vowelae       2.636e+01  2.002e+00   13.166  < 2e-16 ***
## VTRatio:voweli       -3.291e+00  1.688e+00   -1.950 0.051282 .  
## VTRatio:vowelu        1.591e+00  1.737e+00    0.916 0.359832    
## I(VTRatio^2):vowela  -6.550e+00  1.930e+00   -3.393 0.000701 ***
## I(VTRatio^2):vowelae -2.774e+01  2.184e+00  -12.705  < 2e-16 ***
## I(VTRatio^2):voweli   3.416e+00  1.854e+00    1.842 0.065543 .  
## I(VTRatio^2):vowelu  -2.229e+00  1.910e+00   -1.167 0.243266    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.05874 on 2982 degrees of freedom
## Multiple R-squared:  0.9665, Adjusted R-squared:  0.9663 
## F-statistic:  5065 on 17 and 2982 DF,  p-value: < 2.2e-16
##                      Df Sum Sq Mean Sq F value   Pr(>F)    
## VTRatio               1    0.9    0.88   8.168  0.00429 ** 
## I(VTRatio^2)          1   26.8   26.82 250.257  < 2e-16 ***
## vowel                 4  366.4   91.61 854.663  < 2e-16 ***
## replication           1    0.1    0.10   0.898  0.34338    
## generation            1    4.7    4.70  43.824 4.24e-11 ***
## VTRatio:vowel         4   75.2   18.80 175.423  < 2e-16 ***
## I(VTRatio^2):vowel    4    3.5    0.87   8.080 1.78e-06 ***
## Residuals          2983  319.7    0.11                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = hyoidx.m0)
## 
## $vowel
##                 diff         lwr         upr     p adj
## a-schwa  -0.44935250 -0.50094467 -0.39776033 0.0000000
## ae-schwa -0.31538428 -0.36697645 -0.26379212 0.0000000
## i-schwa   0.42960743  0.37801526  0.48119960 0.0000000
## u-schwa   0.35222135  0.30062918  0.40381352 0.0000000
## ae-a      0.13396822  0.08237605  0.18556038 0.0000000
## i-a       0.87895993  0.82736776  0.93055210 0.0000000
## u-a       0.80157385  0.74998169  0.85316602 0.0000000
## i-ae      0.74499171  0.69339955  0.79658388 0.0000000
## u-ae      0.66760563  0.61601347  0.71919780 0.0000000
## u-i      -0.07738608 -0.12897825 -0.02579391 0.0004183
## 
## Call:
## lm(formula = hyoidX ~ VTRatio + I(VTRatio^2) + vowel + (VTRatio:vowel) + 
##     (I(VTRatio^2):vowel) + replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.10914 -0.17807 -0.01253  0.18390  1.35190 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          -1.857e+01  1.535e+00 -12.093  < 2e-16 ***
## VTRatio               7.552e+01  6.797e+00  11.110  < 2e-16 ***
## I(VTRatio^2)         -7.876e+01  7.473e+00 -10.539  < 2e-16 ***
## vowela                9.301e+00  2.211e+00   4.208 2.66e-05 ***
## vowelae               2.736e-01  2.497e+00   0.110 0.912768    
## voweli                1.252e+01  2.114e+00   5.925 3.48e-09 ***
## vowelu                9.679e+00  2.170e+00   4.460 8.51e-06 ***
## replication          -2.310e-04  2.071e-04  -1.115 0.264778    
## generation           -4.986e-04  6.332e-05  -7.874 4.77e-15 ***
## VTRatio:vowela       -4.353e+01  9.787e+00  -4.447 9.01e-06 ***
## VTRatio:vowelae      -1.140e+00  1.099e+01  -0.104 0.917365    
## VTRatio:voweli       -4.416e+01  9.362e+00  -4.716 2.51e-06 ***
## VTRatio:vowelu       -3.686e+01  9.621e+00  -3.831 0.000130 ***
## I(VTRatio^2):vowela   4.820e+01  1.075e+01   4.484 7.59e-06 ***
## I(VTRatio^2):vowelae -4.681e-01  1.200e+01  -0.039 0.968877    
## I(VTRatio^2):voweli   3.812e+01  1.029e+01   3.704 0.000216 ***
## I(VTRatio^2):vowelu   3.570e+01  1.058e+01   3.374 0.000749 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3274 on 2983 degrees of freedom
## Multiple R-squared:  0.599,  Adjusted R-squared:  0.5968 
## F-statistic: 278.5 on 16 and 2983 DF,  p-value: < 2.2e-16
##                      Df Sum Sq Mean Sq   F value Pr(>F)    
## VTRatio               1  952.5   952.5 51207.052 <2e-16 ***
## I(VTRatio^2)          1   26.8    26.8  1442.053 <2e-16 ***
## vowel                 4    6.5     1.6    87.435 <2e-16 ***
## replication           1    0.0     0.0     0.066 0.7970    
## generation            1    0.1     0.1     6.524 0.0107 *  
## VTRatio:vowel         4    2.3     0.6    30.848 <2e-16 ***
## I(VTRatio^2):vowel    4    2.0     0.5    26.573 <2e-16 ***
## Residuals          2983   55.5     0.0                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = hyoidy.m0)
## 
## $vowel
##                  diff         lwr          upr     p adj
## a-schwa   0.001888475 -0.01960401  0.023380961 0.9992698
## ae-schwa  0.065949961  0.04445747  0.087442446 0.0000000
## i-schwa  -0.031287140 -0.05277963 -0.009794654 0.0006920
## u-schwa  -0.076136566 -0.09762905 -0.054644081 0.0000000
## ae-a      0.064061486  0.04256900  0.085553971 0.0000000
## i-a      -0.033175615 -0.05466810 -0.011683129 0.0002509
## u-a      -0.078025041 -0.09951753 -0.056532556 0.0000000
## i-ae     -0.097237100 -0.11872959 -0.075744615 0.0000000
## u-ae     -0.142086527 -0.16357901 -0.120594041 0.0000000
## u-i      -0.044849427 -0.06634191 -0.023356941 0.0000001
## 
## Call:
## lm(formula = hyoidY ~ VTRatio + I(VTRatio^2) + vowel + (VTRatio:vowel) + 
##     (I(VTRatio^2):vowel) + replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.53366 -0.10754  0.00337  0.09817  0.35263 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          -2.541e+01  6.395e-01 -39.735  < 2e-16 ***
## VTRatio               7.866e+01  2.832e+00  27.781  < 2e-16 ***
## I(VTRatio^2)         -7.140e+01  3.113e+00 -22.936  < 2e-16 ***
## vowela                2.613e+00  9.209e-01   2.837  0.00458 ** 
## vowelae               1.107e+01  1.040e+00  10.640  < 2e-16 ***
## voweli                4.913e+00  8.805e-01   5.581 2.61e-08 ***
## vowelu                5.565e+00  9.041e-01   6.155 8.51e-10 ***
## replication           2.900e-05  8.629e-05   0.336  0.73683    
## generation           -2.828e-05  2.638e-05  -1.072  0.28374    
## VTRatio:vowela       -1.101e+01  4.077e+00  -2.702  0.00694 ** 
## VTRatio:vowelae      -4.655e+01  4.577e+00 -10.169  < 2e-16 ***
## VTRatio:voweli       -2.104e+01  3.900e+00  -5.395 7.37e-08 ***
## VTRatio:vowelu       -2.429e+01  4.008e+00  -6.061 1.52e-09 ***
## I(VTRatio^2):vowela   1.148e+01  4.477e+00   2.564  0.01039 *  
## I(VTRatio^2):vowelae  4.870e+01  4.998e+00   9.745  < 2e-16 ***
## I(VTRatio^2):voweli   2.214e+01  4.287e+00   5.164 2.58e-07 ***
## I(VTRatio^2):vowelu   2.589e+01  4.407e+00   5.875 4.68e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1364 on 2983 degrees of freedom
## Multiple R-squared:  0.9469, Adjusted R-squared:  0.9467 
## F-statistic:  3327 on 16 and 2983 DF,  p-value: < 2.2e-16
##                      Df Sum Sq Mean Sq   F value   Pr(>F)    
## VTRatio               1   8830    8830 46330.470  < 2e-16 ***
## I(VTRatio^2)          1     32      32   169.679  < 2e-16 ***
## vowel                 4   2054     514  2694.817  < 2e-16 ***
## replication           1      0       0     0.023    0.879    
## generation            1      3       3    17.459 3.02e-05 ***
## VTRatio:vowel         4    142      36   186.666  < 2e-16 ***
## I(VTRatio^2):vowel    4      9       2    12.036 1.05e-09 ***
## Residuals          2983    568       0                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = pc1art.m0)
## 
## $vowel
##                 diff         lwr        upr     p adj
## a-schwa  -0.84081889 -0.90961292 -0.7720249 0.0000000
## ae-schwa -0.71801444 -0.78680847 -0.6492204 0.0000000
## i-schwa   1.02066711  0.95187308  1.0894611 0.0000000
## u-schwa   1.10377299  1.03497896  1.1725670 0.0000000
## ae-a      0.12280445  0.05401042  0.1915985 0.0000115
## i-a       1.86148599  1.79269197  1.9302800 0.0000000
## u-a       1.94459187  1.87579785  2.0133859 0.0000000
## i-ae      1.73868154  1.66988751  1.8074756 0.0000000
## u-ae      1.82178742  1.75299339  1.8905815 0.0000000
## u-i       0.08310588  0.01431185  0.1518999 0.0087504
## 
## Call:
## lm(formula = PC1.art ~ VTRatio + I(VTRatio^2) + vowel + (VTRatio:vowel) + 
##     (I(VTRatio^2):vowel) + replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.09636 -0.24204  0.02471  0.28500  1.31616 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          -4.227e+01  2.047e+00 -20.648  < 2e-16 ***
## VTRatio               1.409e+02  9.063e+00  15.546  < 2e-16 ***
## I(VTRatio^2)         -1.047e+02  9.965e+00 -10.509  < 2e-16 ***
## vowela                1.394e+01  2.948e+00   4.728 2.37e-06 ***
## vowelae               2.130e+01  3.330e+00   6.396 1.84e-10 ***
## voweli                1.545e+01  2.818e+00   5.481 4.58e-08 ***
## vowelu                8.364e+00  2.894e+00   2.890  0.00388 ** 
## replication           8.537e-05  2.762e-04   0.309  0.75727    
## generation            2.156e-04  8.444e-05   2.553  0.01073 *  
## VTRatio:vowela       -6.467e+01  1.305e+01  -4.955 7.62e-07 ***
## VTRatio:vowelae      -9.104e+01  1.465e+01  -6.214 5.88e-10 ***
## VTRatio:voweli       -5.064e+01  1.248e+01  -4.056 5.11e-05 ***
## VTRatio:vowelu       -2.347e+01  1.283e+01  -1.829  0.06743 .  
## I(VTRatio^2):vowela   7.002e+01  1.433e+01   4.886 1.08e-06 ***
## I(VTRatio^2):vowelae  9.286e+01  1.600e+01   5.805 7.12e-09 ***
## I(VTRatio^2):voweli   4.104e+01  1.372e+01   2.990  0.00281 ** 
## I(VTRatio^2):vowelu   1.615e+01  1.411e+01   1.145  0.25233    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4366 on 2983 degrees of freedom
## Multiple R-squared:  0.9512, Adjusted R-squared:  0.9509 
## F-statistic:  3631 on 16 and 2983 DF,  p-value: < 2.2e-16
##                      Df Sum Sq Mean Sq  F value   Pr(>F)    
## VTRatio               1   1244  1243.6 4571.942  < 2e-16 ***
## I(VTRatio^2)          1     74    74.3  273.331  < 2e-16 ***
## vowel                 4   4283  1070.6 3936.255  < 2e-16 ***
## replication           1      0     0.0    0.007    0.932    
## generation            1      8     7.7   28.354 1.09e-07 ***
## VTRatio:vowel         4    119    29.7  109.359  < 2e-16 ***
## I(VTRatio^2):vowel    4     48    12.0   44.085  < 2e-16 ***
## Residuals          2983    811     0.3                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = pc2art.m0)
## 
## $vowel
##                diff        lwr        upr p adj
## a-schwa  -1.4059747 -1.4881602 -1.3237891     0
## ae-schwa -0.6538564 -0.7360419 -0.5716708     0
## i-schwa   2.0397071  1.9575215  2.1218926     0
## u-schwa   0.8372525  0.7550669  0.9194380     0
## ae-a      0.7521183  0.6699327  0.8343039     0
## i-a       3.4456817  3.3634962  3.5278673     0
## u-a       2.2432272  2.1610416  2.3254127     0
## i-ae      2.6935634  2.6113779  2.7757490     0
## u-ae      1.4911088  1.4089233  1.5732944     0
## u-i      -1.2024546 -1.2846401 -1.1202690     0
## 
## Call:
## lm(formula = PC2.art ~ VTRatio + I(VTRatio^2) + vowel + (VTRatio:vowel) + 
##     (I(VTRatio^2):vowel) + replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.19105 -0.32576 -0.00574  0.35298  1.91107 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          -1.289e+01  2.446e+00  -5.272 1.45e-07 ***
## VTRatio               6.602e+01  1.083e+01   6.098 1.21e-09 ***
## I(VTRatio^2)         -8.252e+01  1.190e+01  -6.932 5.07e-12 ***
## vowela                1.289e+01  3.521e+00   3.661 0.000255 ***
## vowelae               6.460e+00  3.978e+00   1.624 0.104494    
## voweli               -1.817e+01  3.367e+00  -5.396 7.34e-08 ***
## vowelu                1.539e+01  3.457e+00   4.452 8.82e-06 ***
## replication          -5.443e-05  3.300e-04  -0.165 0.868998    
## generation           -5.854e-04  1.009e-04  -5.804 7.17e-09 ***
## VTRatio:vowela       -6.395e+01  1.559e+01  -4.102 4.21e-05 ***
## VTRatio:vowelae      -2.425e+01  1.750e+01  -1.386 0.165939    
## VTRatio:voweli        1.011e+02  1.491e+01   6.780 1.44e-11 ***
## VTRatio:vowelu       -5.818e+01  1.533e+01  -3.797 0.000150 ***
## I(VTRatio^2):vowela   7.094e+01  1.712e+01   4.143 3.52e-05 ***
## I(VTRatio^2):vowelae  1.867e+01  1.911e+01   0.977 0.328643    
## I(VTRatio^2):voweli  -1.237e+02  1.639e+01  -7.542 6.09e-14 ***
## I(VTRatio^2):vowelu   5.716e+01  1.685e+01   3.392 0.000703 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5215 on 2983 degrees of freedom
## Multiple R-squared:  0.8768, Adjusted R-squared:  0.8762 
## F-statistic:  1327 on 16 and 2983 DF,  p-value: < 2.2e-16
##                      Df Sum Sq Mean Sq  F value   Pr(>F)    
## VTRatio               1    144   144.1  328.505  < 2e-16 ***
## I(VTRatio^2)          1     27    26.8   61.090  7.5e-15 ***
## vowel                 4   3305   826.1 1882.811  < 2e-16 ***
## replication           1      0     0.0    0.019 0.889464    
## generation            1      6     6.0   13.702 0.000218 ***
## VTRatio:vowel         4    312    78.1  178.004  < 2e-16 ***
## I(VTRatio^2):vowel    4    252    63.1  143.788  < 2e-16 ***
## Residuals          2983   1309     0.4                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = pc3art.m0)
## 
## $vowel
##                 diff        lwr         upr     p adj
## a-schwa  -0.05569066 -0.1600755  0.04869415 0.5911724
## ae-schwa -1.35562782 -1.4600126 -1.25124301 0.0000000
## i-schwa  -1.60114017 -1.7055250 -1.49675537 0.0000000
## u-schwa   1.29745585  1.1930710  1.40184066 0.0000000
## ae-a     -1.29993716 -1.4043220 -1.19555236 0.0000000
## i-a      -1.54544952 -1.6498343 -1.44106471 0.0000000
## u-a       1.35314651  1.2487617  1.45753131 0.0000000
## i-ae     -0.24551236 -0.3498972 -0.14112755 0.0000000
## u-ae      2.65308367  2.5486989  2.75746847 0.0000000
## u-i       2.89859603  2.7942112  3.00298083 0.0000000
## 
## Call:
## lm(formula = PC3.art ~ VTRatio + I(VTRatio^2) + vowel + (VTRatio:vowel) + 
##     (I(VTRatio^2):vowel) + replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.49396 -0.39220  0.03087  0.44005  2.08533 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          -2.064e+01  3.106e+00  -6.644 3.62e-11 ***
## VTRatio               8.966e+01  1.375e+01   6.519 8.26e-11 ***
## I(VTRatio^2)         -9.447e+01  1.512e+01  -6.248 4.75e-10 ***
## vowela                1.347e+01  4.473e+00   3.011 0.002629 ** 
## vowelae               4.506e+00  5.053e+00   0.892 0.372569    
## voweli                9.287e+01  4.276e+00  21.718  < 2e-16 ***
## vowelu                1.950e+01  4.391e+00   4.442 9.26e-06 ***
## replication           3.698e-05  4.191e-04   0.088 0.929692    
## generation           -3.283e-04  1.281e-04  -2.562 0.010452 *  
## VTRatio:vowela       -5.129e+01  1.980e+01  -2.590 0.009636 ** 
## VTRatio:vowelae      -2.789e+01  2.223e+01  -1.255 0.209699    
## VTRatio:voweli       -4.033e+02  1.894e+01 -21.290  < 2e-16 ***
## VTRatio:vowelu       -6.422e+01  1.947e+01  -3.299 0.000982 ***
## I(VTRatio^2):vowela   4.689e+01  2.175e+01   2.156 0.031152 *  
## I(VTRatio^2):vowelae  3.236e+01  2.427e+01   1.333 0.182587    
## I(VTRatio^2):voweli   4.258e+02  2.082e+01  20.448  < 2e-16 ***
## I(VTRatio^2):vowelu   5.243e+01  2.140e+01   2.450 0.014353 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6624 on 2983 degrees of freedom
## Multiple R-squared:  0.7556, Adjusted R-squared:  0.7543 
## F-statistic: 576.4 on 16 and 2983 DF,  p-value: < 2.2e-16
Summary of regressions of articulators on VT ratio with betas (for non-factor DVs and ‘.’ for factors), p-values, and adjusted R2. Interactions are denoted by ‘:’.
DVs, interactions & R2 JA LP LD TCX TCY TTX TTY TBX TBY HX HY hyoidX hyoidY PC1(art) PC2(art) PC3(art)
VTRatio 2.8e+02 (2.3e-20***) 47 (1.2e-07***) -34 (0.057) 56 (9.3e-10***) 95 (1.4e-41***) -95 (1.7e-08***) -1.7e+02 (1.1e-25***) -78 (0.00067***) -1.3e+02 (2.1e-18***) 43 (2.2e-21***) 79 (3.4e-151***) 76 (4e-28***) 79 (2.9e-151***) 1.4e+02 (1.8e-52***) 66 (1.2e-09***) 90 (8.3e-11***)
VTRatio^2 -2.9e+02 (1.6e-18***) -45 (5.2e-06***) 24 (0.22) -60 (2.4e-09***) -94 (5.5e-34***) 97 (1.4e-07***) 2e+02 (6.8e-29***) 79 (0.0017**) 1.5e+02 (1.2e-18***) -46 (3.2e-20***) -71 (2.6e-107***) -79 (1.6e-25***) -71 (2.3e-107***) -1e+02 (2.2e-25***) -83 (5.1e-12***) -94 (4.7e-10***)
vowel . (2e-199***) . (7.9e-323***) . (0***) . (0***) . (0***) . (1.2e-63***) . (2.2e-71***) . (7.3e-148***) . (0***) . (0***) . (2.6e-70***) . (0***) . (2.4e-70***) . (0***) . (0***) . (0***)
replication 3.1e-05 (0.97) -0.00015 (0.58) -0.00052 (0.33) 0.0003 (0.28) 0.00017 (0.43) -0.00024 (0.64) -0.00018 (0.71) -0.0003 (0.67) -1.4e-05 (0.98) -0.00016 (0.25) 2.8e-05 (0.74) -0.00023 (0.26) 2.9e-05 (0.74) 8.5e-05 (0.76) -5.4e-05 (0.87) 3.7e-05 (0.93)
generation -0.0032 (1.7e-29***) 0.00076 (1.5e-19***) -0.00023 (0.16) -4.7e-05 (0.58) -1.8e-06 (0.98) -0.00042 (0.0072**) 0.0005 (0.00076***) 0.00069 (0.0013**) 8.5e-06 (0.95) -0.00033 (4.5e-15***) -2.8e-05 (0.28) -0.0005 (4.8e-15***) -2.8e-05 (0.28) 0.00022 (0.011*) -0.00059 (7.2e-09***) -0.00033 (0.01*)
VTRatio:vowel . (9.5e-28***) . (3.1e-50***) . (1.7e-41***) . (0***) . (4.5e-230***) . (4.2e-16***) . (1.3e-67***) . (4e-40***) . (4.1e-30***) . (7.7e-136***) . (4e-25***) . (4.1e-135***) . (3.3e-25***) . (6e-143***) . (4.4e-87***) . (6.4e-137***)
VTRatio^2:vowel . (5e-12***) . (0.00017***) . (0.019*) . (1.8e-263***) . (1.5e-60***) . (1.9e-25***) . (2.2e-18***) . (3.2e-13***) . (5.7e-24***) . (1.1e-06***) . (9e-22***) . (1.8e-06***) . (1.1e-21***) . (1.1e-09***) . (5.3e-36***) . (1.5e-112***)
adjusted R2 34.4% 47.4% 49.2% 89.4% 78.2% 18.2% 42.5% 25.7% 55.6% 60.8% 94.7% 59.7% 94.7% 95.1% 87.6% 75.4%
Summary of regressions of articulators on VT ratio with betas (for non-factor DVs and ‘.’ for factors), p-values, and adjusted R2. Interactions are denoted by ‘:’.
DVs, interactions & R2 HY(normalized)
VTRatio 1.3e+02 (0***)
VTRatio^2 -94 (0***)
vowel . (0***)
LEN -2.1 (0***)
replication -9.2e-06 (0.8)
generation -0.00011 (4.9e-23***)
VTRatio:vowel . (3.7e-63***)
VTRatio^2:vowel . (4.8e-48***)
adjusted R2 96.6%
Regression of articulators on VTRatio, vowel and generation for mobile hyoid (with 95%CI); Part I.

Regression of articulators on VTRatio, vowel and generation for mobile hyoid (with 95%CI); Part I.

Regression of articulators on VTRatio, vowel and generation for mobile hyoid (with 95%CI); Part II.

Regression of articulators on VTRatio, vowel and generation for mobile hyoid (with 95%CI); Part II.

Regression of articulators on VTRatio, vowel and generation for mobile hyoid (with 95%CI); Part III.

Regression of articulators on VTRatio, vowel and generation for mobile hyoid (with 95%CI); Part III.

Regression of HY(normalized) on VTRatio, LEN and vowel for mobile hyoid (with 95%CI); Part IV.

Regression of HY(normalized) on VTRatio, LEN and vowel for mobile hyoid (with 95%CI); Part IV.

Acoustics on LEN and articulatory parameters

F1

##                  Df Sum Sq Mean Sq   F value   Pr(>F)    
## LEN               1     11    11.3 1.495e+03  < 2e-16 ***
## I(LEN^2)          1      0     0.5 6.597e+01 6.68e-16 ***
## vowel             4   8907  2226.7 2.949e+05  < 2e-16 ***
## JA                1      1     1.0 1.329e+02  < 2e-16 ***
## LP                1      3     3.5 4.603e+02  < 2e-16 ***
## LD                1      1     1.4 1.847e+02  < 2e-16 ***
## TCX               1      4     4.1 5.387e+02  < 2e-16 ***
## TCY               1      6     5.8 7.661e+02  < 2e-16 ***
## TTX               1      0     0.0 1.500e-02 0.902556    
## TTY               1      2     2.0 2.642e+02  < 2e-16 ***
## TBX               1      0     0.1 9.196e+00 0.002447 ** 
## TBY               1      0     0.3 3.675e+01 1.52e-09 ***
## hyoidX            1      0     0.2 2.558e+01 4.51e-07 ***
## hyoidY            1      1     1.2 1.549e+02  < 2e-16 ***
## replication       1      0     0.0 2.039e+00 0.153394    
## generation        1      1     1.2 1.580e+02  < 2e-16 ***
## LEN:vowel         4      6     1.4 1.844e+02  < 2e-16 ***
## I(LEN^2):vowel    4      6     1.6 2.132e+02  < 2e-16 ***
## vowel:JA          4      2     0.4 5.427e+01  < 2e-16 ***
## vowel:LP          4      2     0.5 6.660e+01  < 2e-16 ***
## vowel:LD          4      1     0.2 2.706e+01  < 2e-16 ***
## vowel:TCX         4      3     0.7 9.281e+01  < 2e-16 ***
## vowel:TCY         4      1     0.2 2.209e+01  < 2e-16 ***
## vowel:TTX         4      1     0.3 4.461e+01  < 2e-16 ***
## vowel:TTY         4      0     0.1 8.290e+00 1.20e-06 ***
## vowel:TBX         4      2     0.4 5.924e+01  < 2e-16 ***
## vowel:TBY         4      2     0.5 6.778e+01  < 2e-16 ***
## vowel:hyoidX      4      1     0.2 3.207e+01  < 2e-16 ***
## vowel:hyoidY      4      1     0.3 3.570e+01  < 2e-16 ***
## LEN:JA            1      0     0.0 5.820e-01 0.445786    
## LEN:LP            1      0     0.1 1.029e+01 0.001355 ** 
## LEN:LD            1      0     0.1 8.336e+00 0.003915 ** 
## LEN:TCX           1      0     0.1 1.215e+01 0.000497 ***
## LEN:TCY           1      0     0.3 3.548e+01 2.89e-09 ***
## LEN:TTX           1      0     0.1 6.789e+00 0.009218 ** 
## LEN:TTY           1      0     0.0 2.420e-01 0.622696    
## LEN:TBX           1      0     0.1 1.205e+01 0.000526 ***
## LEN:TBY           1      0     0.0 7.360e-01 0.390874    
## LEN:hyoidX        1      0     0.0 3.027e+00 0.081999 .  
## LEN:hyoidY        1      0     0.0 1.272e+00 0.259425    
## Residuals      2917     22     0.0                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f1.m0)
## 
## $vowel
##                diff        lwr        upr p adj
## a-schwa   1.2662947  1.2526021  1.2799872     0
## ae-schwa  1.4269103  1.4132178  1.4406029     0
## i-schwa  -2.7444628 -2.7581554 -2.7307703     0
## u-schwa  -2.1558078 -2.1695004 -2.1421153     0
## ae-a      0.1606157  0.1469231  0.1743082     0
## i-a      -4.0107575 -4.0244500 -3.9970650     0
## u-a      -3.4221025 -3.4357950 -3.4084100     0
## i-ae     -4.1713732 -4.1850657 -4.1576806     0
## u-ae     -3.5827182 -3.5964107 -3.5690256     0
## u-i       0.5886550  0.5749625  0.6023475     0
## 
## Call:
## lm(formula = F1 ~ LEN + I(LEN^2) + vowel + JA + LP + LD + TCX + 
##     TCY + TTX + TTY + TBX + TBY + hyoidX + hyoidY + (LEN:vowel) + 
##     (I(LEN^2):vowel) + (JA:vowel) + (LP:vowel) + (LD:vowel) + 
##     (TCX:vowel) + (TCY:vowel) + (TTX:vowel) + (TTY:vowel) + (TBX:vowel) + 
##     (TBY:vowel) + (hyoidX:vowel) + (hyoidY:vowel) + (JA:LEN) + 
##     (LP:LEN) + (LD:LEN) + (TCX:LEN) + (TCY:LEN) + (TTX:LEN) + 
##     (TTY:LEN) + (TBX:LEN) + (TBY:LEN) + (hyoidX:LEN) + (hyoidY:LEN) + 
##     replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.53296 -0.03753  0.00309  0.03962  0.82373 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       3.627e+00  4.086e-01   8.877  < 2e-16 ***
## LEN              -4.799e-01  1.100e-01  -4.363 1.33e-05 ***
## I(LEN^2)         -3.639e-02  8.523e-03  -4.270 2.02e-05 ***
## vowela            1.506e+00  5.554e-01   2.712 0.006724 ** 
## vowelae          -2.072e+00  5.718e-01  -3.624 0.000295 ***
## voweli            2.348e+00  5.572e-01   4.214 2.59e-05 ***
## vowelu            5.143e+00  4.921e-01  10.450  < 2e-16 ***
## JA               -9.598e-03  9.787e-03  -0.981 0.326801    
## LP               -1.103e-01  3.346e-02  -3.298 0.000987 ***
## LD                5.659e-02  1.705e-02   3.319 0.000914 ***
## TCX              -1.515e-01  3.750e-02  -4.039 5.51e-05 ***
## TCY               3.645e-01  5.554e-02   6.564 6.19e-11 ***
## TTX               5.134e-02  2.219e-02   2.313 0.020766 *  
## TTY              -2.515e-02  2.214e-02  -1.136 0.255989    
## TBX              -5.400e-02  1.572e-02  -3.434 0.000603 ***
## TBY              -3.551e-02  2.587e-02  -1.373 0.169983    
## hyoidX           -1.064e-01  4.643e-02  -2.292 0.021968 *  
## hyoidY            8.790e-02  8.347e-02   1.053 0.292427    
## replication       2.569e-05  5.541e-05   0.464 0.642942    
## generation       -1.419e-04  1.915e-05  -7.412 1.62e-13 ***
## LEN:vowela       -6.864e-02  1.363e-01  -0.504 0.614477    
## LEN:vowelae      -1.133e+00  1.409e-01  -8.042 1.27e-15 ***
## LEN:voweli        1.079e+00  1.442e-01   7.484 9.49e-14 ***
## LEN:vowelu        1.532e+00  1.244e-01  12.316  < 2e-16 ***
## I(LEN^2):vowela  -6.401e-03  8.525e-03  -0.751 0.452789    
## I(LEN^2):vowelae -7.704e-02  8.922e-03  -8.635  < 2e-16 ***
## I(LEN^2):voweli   6.603e-02  9.297e-03   7.102 1.54e-12 ***
## I(LEN^2):vowelu   9.076e-02  8.133e-03  11.159  < 2e-16 ***
## vowela:JA        -1.113e-02  4.718e-03  -2.359 0.018399 *  
## vowelae:JA        1.392e-02  6.523e-03   2.134 0.032930 *  
## voweli:JA         1.479e-03  3.901e-03   0.379 0.704684    
## vowelu:JA         1.224e-02  3.203e-03   3.820 0.000136 ***
## vowela:LP        -2.385e-02  1.407e-02  -1.695 0.090181 .  
## vowelae:LP       -1.937e-02  1.642e-02  -1.180 0.238271    
## voweli:LP        -1.684e-02  1.219e-02  -1.381 0.167256    
## vowelu:LP        -1.601e-01  1.191e-02 -13.445  < 2e-16 ***
## vowela:LD        -1.479e-03  6.785e-03  -0.218 0.827474    
## vowelae:LD       -1.738e-02  7.362e-03  -2.360 0.018317 *  
## voweli:LD        -4.769e-03  5.616e-03  -0.849 0.395845    
## vowelu:LD         5.360e-02  6.608e-03   8.112 7.27e-16 ***
## vowela:TCX       -3.681e-02  4.782e-02  -0.770 0.441504    
## vowelae:TCX      -3.665e-02  2.543e-02  -1.442 0.149551    
## voweli:TCX       -4.570e-02  1.723e-02  -2.651 0.008057 ** 
## vowelu:TCX       -3.333e-01  2.280e-02 -14.621  < 2e-16 ***
## vowela:TCY       -1.637e-01  3.105e-02  -5.272 1.45e-07 ***
## vowelae:TCY       1.201e-02  2.130e-02   0.564 0.573027    
## voweli:TCY       -1.333e-01  1.931e-02  -6.905 6.15e-12 ***
## vowelu:TCY        1.031e-01  1.706e-02   6.045 1.69e-09 ***
## vowela:TTX       -2.349e-02  8.124e-03  -2.892 0.003856 ** 
## vowelae:TTX      -6.155e-03  7.849e-03  -0.784 0.433038    
## voweli:TTX        7.714e-03  6.760e-03   1.141 0.253915    
## vowelu:TTX        8.902e-02  7.564e-03  11.769  < 2e-16 ***
## vowela:TTY       -7.500e-02  8.577e-03  -8.744  < 2e-16 ***
## vowelae:TTY      -5.093e-02  1.203e-02  -4.234 2.37e-05 ***
## voweli:TTY       -1.236e-02  7.367e-03  -1.677 0.093580 .  
## vowelu:TTY       -4.567e-04  6.465e-03  -0.071 0.943695    
## vowela:TBX       -8.877e-03  4.701e-03  -1.888 0.059067 .  
## vowelae:TBX       1.421e-03  7.631e-03   0.186 0.852266    
## voweli:TBX       -4.087e-02  7.431e-03  -5.500 4.13e-08 ***
## vowelu:TBX       -3.673e-03  5.373e-03  -0.684 0.494299    
## vowela:TBY       -1.018e-01  8.146e-03 -12.494  < 2e-16 ***
## vowelae:TBY      -5.995e-02  1.415e-02  -4.236 2.35e-05 ***
## voweli:TBY       -2.682e-02  1.366e-02  -1.963 0.049685 *  
## vowelu:TBY        4.946e-02  8.197e-03   6.034 1.80e-09 ***
## vowela:hyoidX    -2.166e-01  1.918e-02 -11.291  < 2e-16 ***
## vowelae:hyoidX   -1.390e-02  1.835e-02  -0.758 0.448742    
## voweli:hyoidX     3.331e-02  1.708e-02   1.951 0.051189 .  
## vowelu:hyoidX    -3.872e-02  1.408e-02  -2.749 0.006010 ** 
## vowela:hyoidY     2.715e-01  3.031e-02   8.960  < 2e-16 ***
## vowelae:hyoidY    1.042e-01  3.023e-02   3.447 0.000576 ***
## voweli:hyoidY     1.231e-01  2.775e-02   4.435 9.54e-06 ***
## vowelu:hyoidY     2.307e-01  2.463e-02   9.369  < 2e-16 ***
## LEN:JA           -7.366e-04  1.235e-03  -0.596 0.551064    
## LEN:LP           -1.480e-02  4.265e-03  -3.469 0.000529 ***
## LEN:LD            6.672e-03  2.101e-03   3.176 0.001511 ** 
## LEN:TCX          -1.704e-02  4.451e-03  -3.828 0.000132 ***
## LEN:TCY           4.589e-02  6.819e-03   6.730 2.03e-11 ***
## LEN:TTX           6.798e-03  2.630e-03   2.585 0.009799 ** 
## LEN:TTY          -2.443e-03  2.609e-03  -0.936 0.349207    
## LEN:TBX          -6.792e-03  1.853e-03  -3.664 0.000252 ***
## LEN:TBY          -3.093e-03  3.011e-03  -1.027 0.304406    
## LEN:hyoidX       -1.102e-02  5.645e-03  -1.952 0.051071 .  
## LEN:hyoidY        1.064e-02  9.430e-03   1.128 0.259425    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.08689 on 2917 degrees of freedom
## Multiple R-squared:  0.9976, Adjusted R-squared:  0.9975 
## F-statistic: 1.449e+04 on 82 and 2917 DF,  p-value: < 2.2e-16
##                  Df Sum Sq Mean Sq F value   Pr(>F)    
## LEN               1  0.405   0.405  43.323 5.48e-11 ***
## I(LEN^2)          1  3.343   3.343 357.744  < 2e-16 ***
## vowel             4  5.456   1.364 145.938  < 2e-16 ***
## JA                1  0.330   0.330  35.336 3.10e-09 ***
## LP                1  0.732   0.732  78.275  < 2e-16 ***
## LD                1  0.272   0.272  29.143 7.26e-08 ***
## TCX               1  0.474   0.474  50.718 1.34e-12 ***
## TCY               1  0.352   0.352  37.701 9.37e-10 ***
## TTX               1  0.108   0.108  11.546 0.000688 ***
## TTY               1  1.306   1.306 139.746  < 2e-16 ***
## TBX               1  0.379   0.379  40.529 2.24e-10 ***
## TBY               1  0.026   0.026   2.747 0.097551 .  
## hyoidX            1  0.059   0.059   6.279 0.012269 *  
## hyoidY            1  0.700   0.700  74.904  < 2e-16 ***
## replication       1  0.040   0.040   4.263 0.039043 *  
## generation        1  1.208   1.208 129.201  < 2e-16 ***
## LEN:vowel         4  8.050   2.012 215.321  < 2e-16 ***
## I(LEN^2):vowel    4  1.483   0.371  39.679  < 2e-16 ***
## vowel:JA          4  0.825   0.206  22.082  < 2e-16 ***
## vowel:LP          4  1.176   0.294  31.470  < 2e-16 ***
## vowel:LD          4  0.371   0.093   9.932 5.56e-08 ***
## vowel:TCX         4  5.086   1.272 136.061  < 2e-16 ***
## vowel:TCY         4  0.405   0.101  10.841 1.01e-08 ***
## vowel:TTX         4  0.823   0.206  22.002  < 2e-16 ***
## vowel:TTY         4  0.143   0.036   3.817 0.004240 ** 
## vowel:TBX         4  0.163   0.041   4.357 0.001629 ** 
## vowel:TBY         4  0.352   0.088   9.403 1.50e-07 ***
## vowel:hyoidX      4  0.114   0.028   3.044 0.016244 *  
## vowel:hyoidY      4  0.992   0.248  26.539  < 2e-16 ***
## LEN:JA            1  0.141   0.141  15.049 0.000107 ***
## LEN:LP            1  0.471   0.471  50.386 1.58e-12 ***
## LEN:LD            1  0.043   0.043   4.616 0.031751 *  
## LEN:TCX           1  0.001   0.001   0.066 0.797549    
## LEN:TCY           1  0.000   0.000   0.022 0.882510    
## LEN:TTX           1  0.190   0.190  20.278 6.96e-06 ***
## LEN:TTY           1  0.206   0.206  22.080 2.74e-06 ***
## LEN:TBX           1  0.065   0.065   6.959 0.008382 ** 
## LEN:TBY           1  0.118   0.118  12.658 0.000380 ***
## LEN:hyoidX        1  0.000   0.000   0.008 0.927060    
## LEN:hyoidY        1  0.203   0.203  21.707 3.32e-06 ***
## Residuals      2917 27.262   0.009                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f1e.m0)
## 
## $vowel
##                  diff          lwr          upr     p adj
## a-schwa   0.054684170  0.039449563  0.069918777 0.0000000
## ae-schwa  0.046145752  0.030911144  0.061380359 0.0000000
## i-schwa   0.022666699  0.007432091  0.037901306 0.0004810
## u-schwa   0.126216379  0.110981772  0.141450986 0.0000000
## ae-a     -0.008538419 -0.023773026  0.006696189 0.5430742
## i-a      -0.032017471 -0.047252079 -0.016782864 0.0000001
## u-a       0.071532209  0.056297602  0.086766816 0.0000000
## i-ae     -0.023479053 -0.038713660 -0.008244445 0.0002583
## u-ae      0.080070628  0.064836020  0.095305235 0.0000000
## u-i       0.103549680  0.088315073  0.118784288 0.0000000
## 
## Call:
## lm(formula = F1.error ~ LEN + I(LEN^2) + vowel + JA + LP + LD + 
##     TCX + TCY + TTX + TTY + TBX + TBY + hyoidX + hyoidY + (LEN:vowel) + 
##     (I(LEN^2):vowel) + (JA:vowel) + (LP:vowel) + (LD:vowel) + 
##     (TCX:vowel) + (TCY:vowel) + (TTX:vowel) + (TTY:vowel) + (TBX:vowel) + 
##     (TBY:vowel) + (hyoidX:vowel) + (hyoidY:vowel) + (JA:LEN) + 
##     (LP:LEN) + (LD:LEN) + (TCX:LEN) + (TCY:LEN) + (TTX:LEN) + 
##     (TTY:LEN) + (TBX:LEN) + (TBY:LEN) + (hyoidX:LEN) + (hyoidY:LEN) + 
##     replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.46693 -0.02616 -0.00258  0.01953  2.10577 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       1.247e+00  4.546e-01   2.744 0.006111 ** 
## LEN               1.315e-01  1.224e-01   1.075 0.282630    
## I(LEN^2)         -1.291e-03  9.483e-03  -0.136 0.891684    
## vowela            8.464e-01  6.180e-01   1.370 0.170915    
## vowelae           1.466e+00  6.362e-01   2.304 0.021278 *  
## voweli            6.089e-01  6.199e-01   0.982 0.326079    
## vowelu            6.017e+00  5.475e-01  10.989  < 2e-16 ***
## JA                1.606e-02  1.089e-02   1.475 0.140368    
## LP               -2.757e-01  3.723e-02  -7.406 1.70e-13 ***
## LD                5.644e-02  1.897e-02   2.975 0.002950 ** 
## TCX              -3.331e-02  4.173e-02  -0.798 0.424734    
## TCY              -6.930e-03  6.179e-02  -0.112 0.910704    
## TTX               9.012e-02  2.469e-02   3.650 0.000267 ***
## TTY              -1.256e-01  2.463e-02  -5.101 3.59e-07 ***
## TBX              -1.248e-02  1.750e-02  -0.713 0.475745    
## TBY               9.211e-02  2.879e-02   3.200 0.001390 ** 
## hyoidX           -7.728e-02  5.165e-02  -1.496 0.134720    
## hyoidY            4.258e-01  9.287e-02   4.584 4.74e-06 ***
## replication       6.110e-05  6.165e-05   0.991 0.321733    
## generation       -1.512e-04  2.131e-05  -7.098 1.59e-12 ***
## LEN:vowela        2.542e-01  1.516e-01   1.677 0.093693 .  
## LEN:vowelae       4.780e-01  1.567e-01   3.049 0.002314 ** 
## LEN:voweli        7.288e-02  1.604e-01   0.454 0.649659    
## LEN:vowelu        1.196e+00  1.384e-01   8.642  < 2e-16 ***
## I(LEN^2):vowela   1.630e-02  9.485e-03   1.719 0.085778 .  
## I(LEN^2):vowelae  3.307e-02  9.927e-03   3.331 0.000875 ***
## I(LEN^2):voweli   4.050e-03  1.034e-02   0.392 0.695442    
## I(LEN^2):vowelu   6.620e-02  9.049e-03   7.315 3.30e-13 ***
## vowela:JA         5.655e-03  5.249e-03   1.077 0.281376    
## vowelae:JA        5.222e-03  7.258e-03   0.720 0.471877    
## voweli:JA         5.632e-03  4.340e-03   1.298 0.194541    
## vowelu:JA         8.979e-03  3.564e-03   2.519 0.011814 *  
## vowela:LP         3.901e-02  1.565e-02   2.492 0.012761 *  
## vowelae:LP        2.302e-02  1.827e-02   1.260 0.207871    
## voweli:LP        -7.583e-03  1.356e-02  -0.559 0.576132    
## vowelu:LP        -1.167e-01  1.325e-02  -8.808  < 2e-16 ***
## vowela:LD        -6.681e-03  7.550e-03  -0.885 0.376281    
## vowelae:LD        5.244e-03  8.191e-03   0.640 0.522083    
## voweli:LD        -4.896e-03  6.248e-03  -0.784 0.433391    
## vowelu:LD         4.064e-02  7.352e-03   5.527 3.54e-08 ***
## vowela:TCX       -4.357e-02  5.320e-02  -0.819 0.412932    
## vowelae:TCX       4.460e-02  2.829e-02   1.577 0.115004    
## voweli:TCX       -2.530e-02  1.918e-02  -1.320 0.187076    
## vowelu:TCX       -3.503e-01  2.537e-02 -13.811  < 2e-16 ***
## vowela:TCY        1.578e-02  3.454e-02   0.457 0.647766    
## vowelae:TCY       2.750e-02  2.370e-02   1.160 0.245944    
## voweli:TCY       -3.996e-02  2.148e-02  -1.861 0.062914 .  
## vowelu:TCY        1.012e-01  1.898e-02   5.332 1.05e-07 ***
## vowela:TTX        1.168e-02  9.039e-03   1.293 0.196223    
## vowelae:TTX       3.062e-03  8.733e-03   0.351 0.725854    
## voweli:TTX       -4.000e-03  7.521e-03  -0.532 0.594866    
## vowelu:TTX        6.223e-02  8.416e-03   7.395 1.84e-13 ***
## vowela:TTY        4.608e-02  9.543e-03   4.829 1.44e-06 ***
## vowelae:TTY       5.214e-02  1.339e-02   3.895 0.000100 ***
## voweli:TTY        7.995e-03  8.196e-03   0.975 0.329449    
## vowelu:TTY        1.762e-03  7.193e-03   0.245 0.806467    
## vowela:TBX       -6.060e-03  5.230e-03  -1.159 0.246660    
## vowelae:TBX      -1.227e-02  8.490e-03  -1.446 0.148370    
## voweli:TBX       -5.075e-03  8.268e-03  -0.614 0.539426    
## vowelu:TBX       -4.705e-04  5.978e-03  -0.079 0.937279    
## vowela:TBY        5.368e-02  9.063e-03   5.922 3.54e-09 ***
## vowelae:TBY       3.287e-02  1.575e-02   2.087 0.036948 *  
## voweli:TBY       -1.572e-03  1.520e-02  -0.103 0.917647    
## vowelu:TBY        2.940e-02  9.120e-03   3.224 0.001280 ** 
## vowela:hyoidX     8.941e-02  2.135e-02   4.189 2.89e-05 ***
## vowelae:hyoidX    2.922e-02  2.042e-02   1.431 0.152546    
## voweli:hyoidX     3.794e-02  1.900e-02   1.997 0.045940 *  
## vowelu:hyoidX    -6.644e-03  1.567e-02  -0.424 0.671622    
## vowela:hyoidY    -9.291e-02  3.372e-02  -2.755 0.005901 ** 
## vowelae:hyoidY   -8.269e-02  3.363e-02  -2.459 0.014007 *  
## voweli:hyoidY     4.283e-02  3.088e-02   1.387 0.165492    
## vowelu:hyoidY     1.547e-01  2.740e-02   5.644 1.82e-08 ***
## LEN:JA            2.751e-03  1.375e-03   2.001 0.045464 *  
## LEN:LP           -3.597e-02  4.746e-03  -7.580 4.63e-14 ***
## LEN:LD            6.877e-03  2.338e-03   2.942 0.003288 ** 
## LEN:TCX          -5.084e-03  4.953e-03  -1.027 0.304739    
## LEN:TCY          -9.980e-04  7.587e-03  -0.132 0.895357    
## LEN:TTX           1.097e-02  2.927e-03   3.749 0.000181 ***
## LEN:TTY          -1.410e-02  2.903e-03  -4.857 1.26e-06 ***
## LEN:TBX          -2.257e-03  2.062e-03  -1.094 0.273865    
## LEN:TBY           1.102e-02  3.350e-03   3.290 0.001012 ** 
## LEN:hyoidX       -7.254e-03  6.281e-03  -1.155 0.248255    
## LEN:hyoidY        4.888e-02  1.049e-02   4.659 3.32e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.09667 on 2917 degrees of freedom
## Multiple R-squared:  0.5732, Adjusted R-squared:  0.5612 
## F-statistic: 47.77 on 82 and 2917 DF,  p-value: < 2.2e-16

F2

##                  Df Sum Sq Mean Sq   F value   Pr(>F)    
## LEN               1     44      44 3.106e+03  < 2e-16 ***
## I(LEN^2)          1      7       7 4.818e+02  < 2e-16 ***
## vowel             4  25939    6485 4.553e+05  < 2e-16 ***
## JA                1      1       1 6.160e+01 5.86e-15 ***
## LP                1      0       0 1.907e+01 1.30e-05 ***
## LD                1      0       0 1.497e+01 0.000112 ***
## TCX               1     16      16 1.090e+03  < 2e-16 ***
## TCY               1     15      15 1.074e+03  < 2e-16 ***
## TTX               1      2       2 1.113e+02  < 2e-16 ***
## TTY               1      1       1 1.005e+02  < 2e-16 ***
## TBX               1      0       0 2.547e+00 0.110640    
## TBY               1      1       1 9.772e+01  < 2e-16 ***
## hyoidX            1      3       3 2.021e+02  < 2e-16 ***
## hyoidY            1      0       0 1.526e+00 0.216762    
## replication       1      0       0 9.600e-02 0.757237    
## generation        1      1       1 5.084e+01 1.26e-12 ***
## LEN:vowel         4     30       7 5.257e+02  < 2e-16 ***
## I(LEN^2):vowel    4     27       7 4.660e+02  < 2e-16 ***
## vowel:JA          4      1       0 2.228e+01  < 2e-16 ***
## vowel:LP          4      0       0 6.827e+00 1.82e-05 ***
## vowel:LD          4      1       0 1.718e+01 6.16e-14 ***
## vowel:TCX         4      3       1 5.149e+01  < 2e-16 ***
## vowel:TCY         4      3       1 5.723e+01  < 2e-16 ***
## vowel:TTX         4      0       0 2.176e+00 0.069206 .  
## vowel:TTY         4      1       0 1.635e+01 2.96e-13 ***
## vowel:TBX         4      0       0 7.635e+00 4.07e-06 ***
## vowel:TBY         4      0       0 2.802e+00 0.024523 *  
## vowel:hyoidX      4      1       0 1.178e+01 1.73e-09 ***
## vowel:hyoidY      4      1       0 1.338e+01 8.30e-11 ***
## LEN:JA            1      0       0 6.376e+00 0.011619 *  
## LEN:LP            1      0       0 3.152e+01 2.15e-08 ***
## LEN:LD            1      0       0 2.033e+00 0.154002    
## LEN:TCX           1      1       1 5.294e+01 4.40e-13 ***
## LEN:TCY           1      0       0 2.556e+01 4.55e-07 ***
## LEN:TTX           1      1       1 3.991e+01 3.06e-10 ***
## LEN:TTY           1      0       0 3.120e-01 0.576711    
## LEN:TBX           1      0       0 8.200e-02 0.774757    
## LEN:TBY           1      0       0 2.304e+00 0.129133    
## LEN:hyoidX        1      0       0 1.371e+00 0.241815    
## LEN:hyoidY        1      0       0 5.316e+00 0.021200 *  
## Residuals      2917     42       0                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f2.m0)
## 
## $vowel
##               diff       lwr       upr p adj
## a-schwa  -1.076651 -1.095457 -1.057844     0
## ae-schwa  2.404134  2.385327  2.422940     0
## i-schwa   4.196537  4.177731  4.215344     0
## u-schwa  -4.353799 -4.372605 -4.334992     0
## ae-a      3.480784  3.461978  3.499591     0
## i-a       5.273188  5.254381  5.291995     0
## u-a      -3.277148 -3.295955 -3.258342     0
## i-ae      1.792404  1.773597  1.811210     0
## u-ae     -6.757933 -6.776739 -6.739126     0
## u-i      -8.550336 -8.569143 -8.531530     0
## 
## Call:
## lm(formula = F2 ~ LEN + I(LEN^2) + vowel + JA + LP + LD + TCX + 
##     TCY + TTX + TTY + TBX + TBY + hyoidX + hyoidY + (LEN:vowel) + 
##     (I(LEN^2):vowel) + (JA:vowel) + (LP:vowel) + (LD:vowel) + 
##     (TCX:vowel) + (TCY:vowel) + (TTX:vowel) + (TTY:vowel) + (TBX:vowel) + 
##     (TBY:vowel) + (hyoidX:vowel) + (hyoidY:vowel) + (JA:LEN) + 
##     (LP:LEN) + (LD:LEN) + (TCX:LEN) + (TCY:LEN) + (TTX:LEN) + 
##     (TTY:LEN) + (TBX:LEN) + (TBY:LEN) + (hyoidX:LEN) + (hyoidY:LEN) + 
##     replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.73512 -0.04835 -0.00327  0.04929  1.19591 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       1.013e+01  5.612e-01  18.057  < 2e-16 ***
## LEN               1.271e-01  1.511e-01   0.841 0.400306    
## I(LEN^2)          8.694e-03  1.171e-02   0.743 0.457721    
## vowela           -2.393e+00  7.629e-01  -3.137 0.001723 ** 
## vowelae          -3.140e+00  7.853e-01  -3.998 6.53e-05 ***
## voweli           -1.183e+01  7.653e-01 -15.462  < 2e-16 ***
## vowelu           -5.871e-01  6.759e-01  -0.869 0.385166    
## JA                1.788e-02  1.344e-02   1.330 0.183633    
## LP               -2.739e-01  4.596e-02  -5.960 2.83e-09 ***
## LD                4.689e-02  2.342e-02   2.003 0.045313 *  
## TCX               3.954e-01  5.151e-02   7.676 2.22e-14 ***
## TCY              -2.208e-01  7.628e-02  -2.894 0.003827 ** 
## TTX               1.696e-01  3.048e-02   5.564 2.88e-08 ***
## TTY               4.945e-03  3.040e-02   0.163 0.870813    
## TBX              -9.730e-03  2.160e-02  -0.451 0.652373    
## TBY              -4.184e-02  3.553e-02  -1.178 0.239057    
## hyoidX           -1.238e-01  6.377e-02  -1.942 0.052205 .  
## hyoidY            2.752e-01  1.147e-01   2.400 0.016450 *  
## replication       1.054e-04  7.610e-05   1.386 0.166006    
## generation       -6.363e-05  2.630e-05  -2.419 0.015624 *  
## LEN:vowela       -2.469e-01  1.872e-01  -1.319 0.187144    
## LEN:vowelae      -1.424e+00  1.935e-01  -7.358 2.42e-13 ***
## LEN:voweli       -4.738e+00  1.980e-01 -23.924  < 2e-16 ***
## LEN:vowelu        7.421e-01  1.709e-01   4.343 1.45e-05 ***
## I(LEN^2):vowela  -1.244e-02  1.171e-02  -1.063 0.288030    
## I(LEN^2):vowelae -9.495e-02  1.225e-02  -7.748 1.28e-14 ***
## I(LEN^2):voweli  -3.242e-01  1.277e-02 -25.387  < 2e-16 ***
## I(LEN^2):vowelu   3.580e-02  1.117e-02   3.205 0.001366 ** 
## vowela:JA        -9.155e-03  6.479e-03  -1.413 0.157792    
## vowelae:JA       -4.783e-03  8.960e-03  -0.534 0.593510    
## voweli:JA        -1.794e-02  5.358e-03  -3.349 0.000822 ***
## vowelu:JA         1.784e-02  4.400e-03   4.055 5.15e-05 ***
## vowela:LP        -2.378e-02  1.933e-02  -1.230 0.218617    
## vowelae:LP        8.153e-03  2.256e-02   0.361 0.717823    
## voweli:LP         3.498e-04  1.674e-02   0.021 0.983333    
## vowelu:LP        -1.024e-01  1.636e-02  -6.262 4.37e-10 ***
## vowela:LD         9.722e-03  9.320e-03   1.043 0.296959    
## vowelae:LD       -8.466e-03  1.011e-02  -0.837 0.402486    
## voweli:LD         1.283e-02  7.713e-03   1.663 0.096457 .  
## vowelu:LD         5.704e-02  9.076e-03   6.285 3.78e-10 ***
## vowela:TCX        1.706e-01  6.568e-02   2.597 0.009448 ** 
## vowelae:TCX      -2.160e-02  3.492e-02  -0.619 0.536216    
## voweli:TCX       -1.562e-01  2.367e-02  -6.598 4.95e-11 ***
## vowelu:TCX        1.263e-01  3.131e-02   4.034 5.63e-05 ***
## vowela:TCY        1.821e-01  4.264e-02   4.270 2.01e-05 ***
## vowelae:TCY       5.105e-04  2.925e-02   0.017 0.986078    
## voweli:TCY        1.924e-01  2.652e-02   7.256 5.10e-13 ***
## vowelu:TCY       -2.325e-01  2.343e-02  -9.925  < 2e-16 ***
## vowela:TTX        3.183e-02  1.116e-02   2.853 0.004361 ** 
## vowelae:TTX       1.021e-02  1.078e-02   0.947 0.343615    
## voweli:TTX        3.059e-03  9.285e-03   0.329 0.741808    
## vowelu:TTX        2.484e-02  1.039e-02   2.391 0.016871 *  
## vowela:TTY        3.022e-02  1.178e-02   2.565 0.010354 *  
## vowelae:TTY       9.534e-04  1.652e-02   0.058 0.953995    
## voweli:TTY       -1.413e-02  1.012e-02  -1.396 0.162805    
## vowelu:TTY       -4.181e-02  8.880e-03  -4.708 2.61e-06 ***
## vowela:TBX        5.047e-04  6.456e-03   0.078 0.937694    
## vowelae:TBX       1.393e-02  1.048e-02   1.329 0.184020    
## voweli:TBX       -3.847e-02  1.021e-02  -3.769 0.000167 ***
## vowelu:TBX        9.269e-03  7.380e-03   1.256 0.209247    
## vowela:TBY        4.014e-02  1.119e-02   3.588 0.000339 ***
## vowelae:TBY       1.785e-02  1.944e-02   0.918 0.358732    
## voweli:TBY        4.236e-02  1.876e-02   2.258 0.024033 *  
## vowelu:TBY        2.772e-02  1.126e-02   2.462 0.013860 *  
## vowela:hyoidX     1.145e-01  2.635e-02   4.345 1.44e-05 ***
## vowelae:hyoidX   -1.994e-02  2.520e-02  -0.791 0.428994    
## voweli:hyoidX     1.383e-01  2.345e-02   5.897 4.12e-09 ***
## vowelu:hyoidX     7.140e-02  1.935e-02   3.691 0.000228 ***
## vowela:hyoidY    -1.660e-01  4.163e-02  -3.988 6.82e-05 ***
## vowelae:hyoidY   -5.119e-02  4.152e-02  -1.233 0.217708    
## voweli:hyoidY     1.080e-01  3.812e-02   2.835 0.004621 ** 
## vowelu:hyoidY     9.503e-02  3.383e-02   2.809 0.004998 ** 
## LEN:JA            2.331e-03  1.697e-03   1.374 0.169568    
## LEN:LP           -3.700e-02  5.858e-03  -6.316 3.10e-10 ***
## LEN:LD            6.480e-03  2.886e-03   2.246 0.024793 *  
## LEN:TCX           4.392e-02  6.114e-03   7.184 8.56e-13 ***
## LEN:TCY          -2.640e-02  9.366e-03  -2.818 0.004859 ** 
## LEN:TTX           2.153e-02  3.613e-03   5.959 2.85e-09 ***
## LEN:TTY          -4.579e-04  3.584e-03  -0.128 0.898353    
## LEN:TBX          -1.750e-03  2.546e-03  -0.688 0.491805    
## LEN:TBY          -7.076e-03  4.136e-03  -1.711 0.087168 .  
## LEN:hyoidX       -1.293e-02  7.754e-03  -1.667 0.095612 .  
## LEN:hyoidY        2.986e-02  1.295e-02   2.306 0.021200 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1193 on 2917 degrees of freedom
## Multiple R-squared:  0.9984, Adjusted R-squared:  0.9984 
## F-statistic: 2.235e+04 on 82 and 2917 DF,  p-value: < 2.2e-16
##                  Df Sum Sq Mean Sq  F value   Pr(>F)    
## LEN               1  19.24  19.236  875.956  < 2e-16 ***
## I(LEN^2)          1  22.38  22.380 1019.106  < 2e-16 ***
## vowel             4  50.08  12.520  570.121  < 2e-16 ***
## JA                1   0.04   0.036    1.630 0.201752    
## LP                1   2.57   2.575  117.250  < 2e-16 ***
## LD                1   1.60   1.601   72.899  < 2e-16 ***
## TCX               1   9.01   9.011  410.324  < 2e-16 ***
## TCY               1   5.91   5.908  269.039  < 2e-16 ***
## TTX               1   0.98   0.976   44.435 3.13e-11 ***
## TTY               1   0.76   0.756   34.426 4.93e-09 ***
## TBX               1   0.07   0.066    3.023 0.082184 .  
## TBY               1   0.09   0.095    4.310 0.037985 *  
## hyoidX            1   5.73   5.735  261.148  < 2e-16 ***
## hyoidY            1   0.17   0.166    7.550 0.006040 ** 
## replication       1   0.00   0.000    0.008 0.930489    
## generation        1   0.73   0.726   33.049 9.91e-09 ***
## LEN:vowel         4  71.25  17.813  811.159  < 2e-16 ***
## I(LEN^2):vowel    4  46.75  11.687  532.188  < 2e-16 ***
## vowel:JA          4   0.80   0.201    9.138 2.47e-07 ***
## vowel:LP          4   0.24   0.059    2.697 0.029257 *  
## vowel:LD          4   0.22   0.054    2.480 0.042049 *  
## vowel:TCX         4   4.14   1.036   47.182  < 2e-16 ***
## vowel:TCY         4   4.34   1.086   49.459  < 2e-16 ***
## vowel:TTX         4   0.17   0.042    1.923 0.103781    
## vowel:TTY         4   0.07   0.018    0.839 0.500080    
## vowel:TBX         4   0.20   0.051    2.303 0.056279 .  
## vowel:TBY         4   0.53   0.133    6.041 7.73e-05 ***
## vowel:hyoidX      4   1.37   0.342   15.552 1.35e-12 ***
## vowel:hyoidY      4   1.41   0.353   16.073 5.04e-13 ***
## LEN:JA            1   1.36   1.359   61.897 5.06e-15 ***
## LEN:LP            1   0.42   0.419   19.082 1.30e-05 ***
## LEN:LD            1   0.76   0.758   34.514 4.71e-09 ***
## LEN:TCX           1   3.20   3.202  145.791  < 2e-16 ***
## LEN:TCY           1   5.47   5.470  249.092  < 2e-16 ***
## LEN:TTX           1   0.00   0.002    0.084 0.772461    
## LEN:TTY           1   0.34   0.345   15.700 7.60e-05 ***
## LEN:TBX           1   0.18   0.176    8.010 0.004683 ** 
## LEN:TBY           1   0.05   0.050    2.265 0.132476    
## LEN:hyoidX        1   0.31   0.315   14.329 0.000157 ***
## LEN:hyoidY        1   0.01   0.008    0.372 0.541912    
## Residuals      2917  64.06   0.022                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f2e.m0)
## 
## $vowel
##                  diff           lwr         upr     p adj
## a-schwa   0.009513431 -0.0138392091  0.03286607 0.8003291
## ae-schwa  0.033145297  0.0097926571  0.05649794 0.0010356
## i-schwa   0.346381443  0.3230288036  0.36973408 0.0000000
## u-schwa   0.084291067  0.0609384271  0.10764371 0.0000000
## ae-a      0.023631866  0.0002792264  0.04698451 0.0456930
## i-a       0.336868013  0.3135153728  0.36022065 0.0000000
## u-a       0.074777636  0.0514249963  0.09813028 0.0000000
## i-ae      0.313236146  0.2898835066  0.33658879 0.0000000
## u-ae      0.051145770  0.0277931301  0.07449841 0.0000000
## u-i      -0.262090376 -0.2854430163 -0.23873774 0.0000000
## 
## Call:
## lm(formula = F2.error ~ LEN + I(LEN^2) + vowel + JA + LP + LD + 
##     TCX + TCY + TTX + TTY + TBX + TBY + hyoidX + hyoidY + (LEN:vowel) + 
##     (I(LEN^2):vowel) + (JA:vowel) + (LP:vowel) + (LD:vowel) + 
##     (TCX:vowel) + (TCY:vowel) + (TTX:vowel) + (TTY:vowel) + (TBX:vowel) + 
##     (TBY:vowel) + (hyoidX:vowel) + (hyoidY:vowel) + (JA:LEN) + 
##     (LP:LEN) + (LD:LEN) + (TCX:LEN) + (TCY:LEN) + (TTX:LEN) + 
##     (TTY:LEN) + (TBX:LEN) + (TBY:LEN) + (hyoidX:LEN) + (hyoidY:LEN) + 
##     replication + generation, data = d)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.5016 -0.0439 -0.0029  0.0367  3.3766 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       3.246e+00  6.968e-01   4.658 3.34e-06 ***
## LEN               1.250e+00  1.876e-01   6.662 3.21e-11 ***
## I(LEN^2)          1.026e-01  1.454e-02   7.060 2.07e-12 ***
## vowela           -7.736e-01  9.473e-01  -0.817 0.414189    
## vowelae          -2.363e+00  9.752e-01  -2.424 0.015426 *  
## voweli            2.760e+01  9.503e-01  29.044  < 2e-16 ***
## vowelu            1.777e+00  8.393e-01   2.117 0.034307 *  
## JA                6.807e-02  1.669e-02   4.078 4.66e-05 ***
## LP               -2.482e-01  5.707e-02  -4.349 1.41e-05 ***
## LD                1.045e-01  2.908e-02   3.593 0.000332 ***
## TCX              -5.411e-01  6.396e-02  -8.461  < 2e-16 ***
## TCY              -1.369e+00  9.472e-02 -14.449  < 2e-16 ***
## TTX              -6.346e-02  3.785e-02  -1.677 0.093678 .  
## TTY              -1.215e-01  3.775e-02  -3.217 0.001309 ** 
## TBX               6.621e-02  2.682e-02   2.469 0.013609 *  
## TBY              -2.016e-02  4.412e-02  -0.457 0.647711    
## hyoidX            2.647e-01  7.918e-02   3.343 0.000838 ***
## hyoidY           -1.439e-01  1.424e-01  -1.011 0.312163    
## replication      -1.481e-04  9.450e-05  -1.568 0.117080    
## generation       -2.006e-04  3.266e-05  -6.141 9.33e-10 ***
## LEN:vowela       -1.841e-01  2.324e-01  -0.792 0.428305    
## LEN:vowelae      -6.812e-01  2.403e-01  -2.835 0.004613 ** 
## LEN:voweli        7.540e+00  2.459e-01  30.659  < 2e-16 ***
## LEN:vowelu        2.250e-01  2.122e-01   1.060 0.289073    
## I(LEN^2):vowela  -6.430e-03  1.454e-02  -0.442 0.658322    
## I(LEN^2):vowelae -4.429e-02  1.522e-02  -2.911 0.003634 ** 
## I(LEN^2):voweli   4.717e-01  1.586e-02  29.749  < 2e-16 ***
## I(LEN^2):vowelu   6.723e-03  1.387e-02   0.485 0.627939    
## vowela:JA        -4.299e-03  8.046e-03  -0.534 0.593175    
## vowelae:JA       -4.631e-03  1.113e-02  -0.416 0.677281    
## voweli:JA         1.474e-02  6.653e-03   2.215 0.026809 *  
## vowelu:JA         1.143e-02  5.463e-03   2.092 0.036490 *  
## vowela:LP         1.420e-02  2.400e-02   0.592 0.554172    
## vowelae:LP       -2.487e-03  2.801e-02  -0.089 0.929268    
## voweli:LP        -6.461e-02  2.079e-02  -3.108 0.001903 ** 
## vowelu:LP        -9.214e-02  2.032e-02  -4.535 5.98e-06 ***
## vowela:LD        -4.691e-03  1.157e-02  -0.405 0.685243    
## vowelae:LD        7.614e-03  1.256e-02   0.606 0.544274    
## voweli:LD         1.012e-02  9.578e-03   1.057 0.290784    
## vowelu:LD         3.873e-02  1.127e-02   3.437 0.000597 ***
## vowela:TCX       -1.254e-01  8.156e-02  -1.538 0.124273    
## vowelae:TCX      -1.395e-01  4.337e-02  -3.217 0.001308 ** 
## voweli:TCX        7.647e-02  2.939e-02   2.601 0.009331 ** 
## vowelu:TCX        2.706e-01  3.888e-02   6.958 4.23e-12 ***
## vowela:TCY       -3.278e-04  5.295e-02  -0.006 0.995061    
## vowelae:TCY       4.131e-02  3.633e-02   1.137 0.255484    
## voweli:TCY        2.152e-01  3.293e-02   6.534 7.51e-11 ***
## vowelu:TCY       -4.033e-01  2.909e-02 -13.862  < 2e-16 ***
## vowela:TTX        1.152e-02  1.386e-02   0.832 0.405625    
## vowelae:TTX       6.091e-03  1.339e-02   0.455 0.649119    
## voweli:TTX        1.649e-02  1.153e-02   1.430 0.152722    
## vowelu:TTX       -1.850e-04  1.290e-02  -0.014 0.988559    
## vowela:TTY       -7.756e-03  1.463e-02  -0.530 0.596008    
## vowelae:TTY      -2.403e-02  2.052e-02  -1.171 0.241564    
## voweli:TTY       -4.146e-03  1.256e-02  -0.330 0.741458    
## vowelu:TTY       -2.033e-02  1.103e-02  -1.844 0.065357 .  
## vowela:TBX       -7.939e-03  8.017e-03  -0.990 0.322145    
## vowelae:TBX      -2.158e-02  1.301e-02  -1.658 0.097418 .  
## voweli:TBX        1.373e-02  1.267e-02   1.083 0.278795    
## vowelu:TBX        4.656e-03  9.164e-03   0.508 0.611455    
## vowela:TBY       -2.265e-02  1.389e-02  -1.630 0.103210    
## vowelae:TBY      -8.331e-02  2.414e-02  -3.451 0.000566 ***
## voweli:TBY        5.396e-02  2.330e-02   2.316 0.020623 *  
## vowelu:TBY       -4.019e-03  1.398e-02  -0.287 0.773767    
## vowela:hyoidX    -4.755e-03  3.272e-02  -0.145 0.884452    
## vowelae:hyoidX    3.272e-02  3.130e-02   1.046 0.295840    
## voweli:hyoidX    -1.441e-01  2.912e-02  -4.948 7.93e-07 ***
## vowelu:hyoidX     4.644e-02  2.402e-02   1.933 0.053286 .  
## vowela:hyoidY     7.455e-02  5.169e-02   1.442 0.149340    
## vowelae:hyoidY    3.854e-02  5.156e-02   0.748 0.454782    
## voweli:hyoidY    -4.060e-01  4.733e-02  -8.578  < 2e-16 ***
## vowelu:hyoidY     1.583e-01  4.200e-02   3.769 0.000167 ***
## LEN:JA            9.307e-03  2.107e-03   4.417 1.04e-05 ***
## LEN:LP           -3.405e-02  7.275e-03  -4.680 2.99e-06 ***
## LEN:LD            1.398e-02  3.583e-03   3.902 9.74e-05 ***
## LEN:TCX          -7.981e-02  7.592e-03 -10.512  < 2e-16 ***
## LEN:TCY          -1.756e-01  1.163e-02 -15.097  < 2e-16 ***
## LEN:TTX          -7.352e-03  4.486e-03  -1.639 0.101354    
## LEN:TTY          -1.691e-02  4.450e-03  -3.800 0.000147 ***
## LEN:TBX           6.705e-03  3.161e-03   2.121 0.033998 *  
## LEN:TBY          -6.284e-03  5.135e-03  -1.224 0.221122    
## LEN:hyoidX        3.682e-02  9.628e-03   3.824 0.000134 ***
## LEN:hyoidY       -9.811e-03  1.608e-02  -0.610 0.541912    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1482 on 2917 degrees of freedom
## Multiple R-squared:  0.8041, Adjusted R-squared:  0.7986 
## F-statistic:   146 on 82 and 2917 DF,  p-value: < 2.2e-16

F3

##                  Df Sum Sq Mean Sq  F value   Pr(>F)    
## LEN               1  213.5  213.47 3483.358  < 2e-16 ***
## I(LEN^2)          1   94.8   94.78 1546.505  < 2e-16 ***
## vowel             4  397.4   99.36 1621.306  < 2e-16 ***
## JA                1    1.0    1.02   16.594 4.75e-05 ***
## LP                1    0.3    0.28    4.543 0.033136 *  
## LD                1    0.5    0.51    8.366 0.003851 ** 
## TCX               1   12.9   12.87  210.084  < 2e-16 ***
## TCY               1    0.8    0.79   12.945 0.000326 ***
## TTX               1    0.3    0.26    4.175 0.041114 *  
## TTY               1    0.4    0.45    7.265 0.007072 ** 
## TBX               1    4.6    4.55   74.323  < 2e-16 ***
## TBY               1    0.0    0.00    0.030 0.863189    
## hyoidX            1    0.4    0.43    6.990 0.008240 ** 
## hyoidY            1    2.2    2.15   35.163 3.39e-09 ***
## replication       1    0.0    0.01    0.242 0.622858    
## generation        1    0.3    0.31    5.105 0.023933 *  
## LEN:vowel         4   16.2    4.06   66.235  < 2e-16 ***
## I(LEN^2):vowel    4   26.1    6.53  106.505  < 2e-16 ***
## vowel:JA          4    2.9    0.73   11.916 1.32e-09 ***
## vowel:LP          4    0.9    0.24    3.845 0.004040 ** 
## vowel:LD          4    1.4    0.35    5.737 0.000135 ***
## vowel:TCX         4    1.8    0.45    7.307 7.48e-06 ***
## vowel:TCY         4   18.1    4.52   73.781  < 2e-16 ***
## vowel:TTX         4    0.3    0.08    1.282 0.274583    
## vowel:TTY         4    1.7    0.43    6.980 1.37e-05 ***
## vowel:TBX         4    0.6    0.15    2.399 0.048097 *  
## vowel:TBY         4    1.6    0.39    6.413 3.90e-05 ***
## vowel:hyoidX      4    1.2    0.30    4.840 0.000686 ***
## vowel:hyoidY      4   16.5    4.13   67.379  < 2e-16 ***
## LEN:JA            1    2.5    2.51   40.962 1.80e-10 ***
## LEN:LP            1    1.5    1.53   25.034 5.97e-07 ***
## LEN:LD            1    0.6    0.62   10.102 0.001497 ** 
## LEN:TCX           1    4.9    4.93   80.428  < 2e-16 ***
## LEN:TCY           1    0.0    0.01    0.106 0.744228    
## LEN:TTX           1    3.2    3.20   52.192 6.39e-13 ***
## LEN:TTY           1   13.7   13.70  223.579  < 2e-16 ***
## LEN:TBX           1    0.1    0.13    2.084 0.148920    
## LEN:TBY           1    2.6    2.57   41.928 1.11e-10 ***
## LEN:hyoidX        1    0.0    0.03    0.507 0.476542    
## LEN:hyoidY        1    0.1    0.07    1.089 0.296855    
## Residuals      2917  178.8    0.06                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f3.m0)
## 
## $vowel
##                diff         lwr        upr p adj
## a-schwa   0.3796662  0.34065470  0.4186776     0
## ae-schwa  0.1479860  0.10897454  0.1869975     0
## i-schwa   1.0587442  1.01973270  1.0977556     0
## u-schwa   0.4722282  0.43321670  0.5112396     0
## ae-a     -0.2316802 -0.27069163 -0.1926687     0
## i-a       0.6790780  0.64006654  0.7180895     0
## u-a       0.0925620  0.05355054  0.1315735     0
## i-ae      0.9107582  0.87174670  0.9497696     0
## u-ae      0.3242422  0.28523070  0.3632536     0
## u-i      -0.5865160 -0.62552746 -0.5475045     0
## 
## Call:
## lm(formula = F3 ~ LEN + I(LEN^2) + vowel + JA + LP + LD + TCX + 
##     TCY + TTX + TTY + TBX + TBY + hyoidX + hyoidY + (LEN:vowel) + 
##     (I(LEN^2):vowel) + (JA:vowel) + (LP:vowel) + (LD:vowel) + 
##     (TCX:vowel) + (TCY:vowel) + (TTX:vowel) + (TTY:vowel) + (TBX:vowel) + 
##     (TBY:vowel) + (hyoidX:vowel) + (hyoidY:vowel) + (JA:LEN) + 
##     (LP:LEN) + (LD:LEN) + (TCX:LEN) + (TCY:LEN) + (TTX:LEN) + 
##     (TTY:LEN) + (TBX:LEN) + (TBY:LEN) + (hyoidX:LEN) + (hyoidY:LEN) + 
##     replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.60457 -0.09779  0.00112  0.09471  1.52082 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       3.958e+00  1.164e+00   3.400 0.000683 ***
## LEN              -3.057e+00  3.134e-01  -9.756  < 2e-16 ***
## I(LEN^2)         -1.997e-01  2.428e-02  -8.224 2.93e-16 ***
## vowela           -9.245e-01  1.582e+00  -0.584 0.559123    
## vowelae           3.100e+00  1.629e+00   1.903 0.057147 .  
## voweli           -4.323e+00  1.587e+00  -2.723 0.006498 ** 
## vowelu            1.375e+01  1.402e+00   9.810  < 2e-16 ***
## JA                1.311e-01  2.788e-02   4.703 2.68e-06 ***
## LP               -6.471e-01  9.533e-02  -6.787 1.38e-11 ***
## LD                2.400e-01  4.857e-02   4.941 8.22e-07 ***
## TCX               5.104e-01  1.068e-01   4.777 1.87e-06 ***
## TCY               4.776e-01  1.582e-01   3.019 0.002562 ** 
## TTX               2.282e-01  6.322e-02   3.610 0.000311 ***
## TTY              -9.351e-01  6.307e-02 -14.827  < 2e-16 ***
## TBX              -1.497e-01  4.480e-02  -3.342 0.000841 ***
## TBY              -4.229e-01  7.371e-02  -5.737 1.06e-08 ***
## hyoidX            6.326e-02  1.323e-01   0.478 0.632526    
## hyoidY            9.316e-02  2.378e-01   0.392 0.695297    
## replication       3.126e-05  1.579e-04   0.198 0.843029    
## generation       -4.091e-05  5.456e-05  -0.750 0.453389    
## LEN:vowela       -3.467e-01  3.882e-01  -0.893 0.371976    
## LEN:vowelae       1.088e+00  4.014e-01   2.711 0.006751 ** 
## LEN:voweli       -1.044e+00  4.108e-01  -2.541 0.011097 *  
## LEN:vowelu        3.868e+00  3.544e-01  10.912  < 2e-16 ***
## I(LEN^2):vowela  -4.474e-02  2.429e-02  -1.842 0.065552 .  
## I(LEN^2):vowelae  8.208e-02  2.542e-02   3.229 0.001256 ** 
## I(LEN^2):voweli  -5.392e-02  2.649e-02  -2.036 0.041871 *  
## I(LEN^2):vowelu   2.086e-01  2.317e-02   9.001  < 2e-16 ***
## vowela:JA         3.138e-03  1.344e-02   0.233 0.815396    
## vowelae:JA        2.257e-02  1.859e-02   1.214 0.224776    
## voweli:JA        -1.814e-02  1.111e-02  -1.632 0.102796    
## vowelu:JA        -1.052e-02  9.127e-03  -1.153 0.248982    
## vowela:LP         1.913e-02  4.009e-02   0.477 0.633303    
## vowelae:LP        1.009e-01  4.679e-02   2.157 0.031085 *  
## voweli:LP         1.886e-02  3.473e-02   0.543 0.587094    
## vowelu:LP         7.091e-02  3.394e-02   2.090 0.036743 *  
## vowela:LD        -2.396e-02  1.933e-02  -1.240 0.215253    
## vowelae:LD       -3.187e-02  2.097e-02  -1.520 0.128729    
## voweli:LD        -9.331e-03  1.600e-02  -0.583 0.559831    
## vowelu:LD        -4.178e-02  1.883e-02  -2.219 0.026574 *  
## vowela:TCX       -8.508e-01  1.362e-01  -6.245 4.86e-10 ***
## vowelae:TCX      -2.094e-02  7.244e-02  -0.289 0.772549    
## voweli:TCX        1.591e-01  4.910e-02   3.240 0.001211 ** 
## vowelu:TCX       -1.404e-01  6.496e-02  -2.161 0.030777 *  
## vowela:TCY       -6.356e-01  8.845e-02  -7.186 8.43e-13 ***
## vowelae:TCY      -1.441e-01  6.068e-02  -2.374 0.017651 *  
## voweli:TCY       -2.382e-01  5.500e-02  -4.330 1.54e-05 ***
## vowelu:TCY        4.001e-01  4.860e-02   8.234 2.70e-16 ***
## vowela:TTX        4.424e-03  2.315e-02   0.191 0.848434    
## vowelae:TTX      -3.155e-02  2.236e-02  -1.411 0.158380    
## voweli:TTX       -3.975e-02  1.926e-02  -2.064 0.039111 *  
## vowelu:TTX       -4.169e-02  2.155e-02  -1.935 0.053136 .  
## vowela:TTY       -1.121e-01  2.444e-02  -4.587 4.68e-06 ***
## vowelae:TTY      -4.285e-02  3.428e-02  -1.250 0.211308    
## voweli:TTY        1.940e-02  2.099e-02   0.925 0.355289    
## vowelu:TTY        7.924e-02  1.842e-02   4.302 1.75e-05 ***
## vowela:TBX       -2.759e-02  1.339e-02  -2.060 0.039475 *  
## vowelae:TBX      -2.295e-02  2.174e-02  -1.056 0.291194    
## voweli:TBX        3.082e-02  2.117e-02   1.456 0.145544    
## vowelu:TBX        3.340e-02  1.531e-02   2.182 0.029210 *  
## vowela:TBY       -6.983e-02  2.321e-02  -3.009 0.002643 ** 
## vowelae:TBY      -1.305e-01  4.033e-02  -3.236 0.001226 ** 
## voweli:TBY       -3.260e-02  3.892e-02  -0.838 0.402262    
## vowelu:TBY       -8.514e-03  2.335e-02  -0.365 0.715481    
## vowela:hyoidX    -3.817e-01  5.466e-02  -6.983 3.57e-12 ***
## vowelae:hyoidX   -1.499e-01  5.228e-02  -2.868 0.004159 ** 
## voweli:hyoidX     1.959e-01  4.865e-02   4.027 5.79e-05 ***
## vowelu:hyoidX    -1.893e-02  4.013e-02  -0.472 0.637117    
## vowela:hyoidY     2.869e-01  8.635e-02   3.322 0.000905 ***
## vowelae:hyoidY   -1.480e-01  8.613e-02  -1.719 0.085776 .  
## voweli:hyoidY    -1.668e-01  7.907e-02  -2.110 0.034966 *  
## vowelu:hyoidY    -1.021e+00  7.017e-02 -14.547  < 2e-16 ***
## LEN:JA            1.866e-02  3.520e-03   5.301 1.24e-07 ***
## LEN:LP           -7.985e-02  1.215e-02  -6.570 5.92e-11 ***
## LEN:LD            2.818e-02  5.986e-03   4.708 2.62e-06 ***
## LEN:TCX           1.001e-01  1.268e-02   7.893 4.12e-15 ***
## LEN:TCY           6.073e-02  1.943e-02   3.126 0.001790 ** 
## LEN:TTX           2.377e-02  7.494e-03   3.172 0.001532 ** 
## LEN:TTY          -1.143e-01  7.434e-03 -15.381  < 2e-16 ***
## LEN:TBX          -2.155e-02  5.280e-03  -4.081 4.60e-05 ***
## LEN:TBY          -5.448e-02  8.578e-03  -6.351 2.47e-10 ***
## LEN:hyoidX        1.499e-02  1.608e-02   0.932 0.351542    
## LEN:hyoidY       -2.803e-02  2.687e-02  -1.043 0.296855    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2476 on 2917 degrees of freedom
## Multiple R-squared:  0.8259, Adjusted R-squared:  0.821 
## F-statistic: 168.7 on 82 and 2917 DF,  p-value: < 2.2e-16
##                  Df Sum Sq Mean Sq  F value   Pr(>F)    
## LEN               1  336.8   336.8 3485.509  < 2e-16 ***
## I(LEN^2)          1  205.5   205.5 2126.484  < 2e-16 ***
## vowel             4   72.2    18.0  186.734  < 2e-16 ***
## JA                1   15.7    15.7  162.741  < 2e-16 ***
## LP                1    0.1     0.1    1.075 0.299992    
## LD                1    1.7     1.7   17.256 3.36e-05 ***
## TCX               1   22.1    22.1  228.788  < 2e-16 ***
## TCY               1    0.2     0.2    2.284 0.130832    
## TTX               1    3.4     3.4   34.903 3.87e-09 ***
## TTY               1   15.9    15.9  164.735  < 2e-16 ***
## TBX               1    8.5     8.5   87.754  < 2e-16 ***
## TBY               1    4.5     4.5   46.123 1.34e-11 ***
## hyoidX            1    0.1     0.1    1.409 0.235356    
## hyoidY            1    5.4     5.4   55.441 1.26e-13 ***
## replication       1    0.0     0.0    0.012 0.911738    
## generation        1    3.9     3.9   40.256 2.57e-10 ***
## LEN:vowel         4   94.7    23.7  244.928  < 2e-16 ***
## I(LEN^2):vowel    4   30.0     7.5   77.687  < 2e-16 ***
## vowel:JA          4    4.2     1.1   10.909 8.85e-09 ***
## vowel:LP          4    4.5     1.1   11.543 2.68e-09 ***
## vowel:LD          4    3.3     0.8    8.595 6.81e-07 ***
## vowel:TCX         4    5.3     1.3   13.642 5.06e-11 ***
## vowel:TCY         4   11.1     2.8   28.630  < 2e-16 ***
## vowel:TTX         4    0.9     0.2    2.236 0.062798 .  
## vowel:TTY         4   14.2     3.5   36.632  < 2e-16 ***
## vowel:TBX         4    1.5     0.4    3.799 0.004377 ** 
## vowel:TBY         4    2.0     0.5    5.246 0.000329 ***
## vowel:hyoidX      4    1.3     0.3    3.326 0.009989 ** 
## vowel:hyoidY      4   18.1     4.5   46.703  < 2e-16 ***
## LEN:JA            1    5.0     5.0   51.525 8.93e-13 ***
## LEN:LP            1    1.0     1.0   10.717 0.001074 ** 
## LEN:LD            1    0.4     0.4    3.973 0.046338 *  
## LEN:TCX           1    8.6     8.6   88.958  < 2e-16 ***
## LEN:TCY           1    0.4     0.4    3.749 0.052923 .  
## LEN:TTX           1    6.4     6.4   66.435 5.31e-16 ***
## LEN:TTY           1    9.1     9.1   94.255  < 2e-16 ***
## LEN:TBX           1    1.8     1.8   18.374 1.87e-05 ***
## LEN:TBY           1    0.3     0.3    3.273 0.070545 .  
## LEN:hyoidX        1    0.4     0.4    4.153 0.041656 *  
## LEN:hyoidY        1    1.4     1.4   14.198 0.000168 ***
## Residuals      2917  281.9     0.1                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f3e.m0)
## 
## $vowel
##                 diff         lwr         upr     p adj
## a-schwa   0.24590068  0.19691401  0.29488734 0.0000000
## ae-schwa  0.01228932 -0.03669735  0.06127598 0.9598124
## i-schwa  -0.02238000 -0.07136667  0.02660666 0.7236744
## u-schwa   0.36119025  0.31220358  0.41017691 0.0000000
## ae-a     -0.23361136 -0.28259802 -0.18462469 0.0000000
## i-a      -0.26828068 -0.31726735 -0.21929401 0.0000000
## u-a       0.11528957  0.06630290  0.16427623 0.0000000
## i-ae     -0.03466932 -0.08365599  0.01431734 0.3006206
## u-ae      0.34890093  0.29991426  0.39788759 0.0000000
## u-i       0.38357025  0.33458358  0.43255691 0.0000000
## 
## Call:
## lm(formula = F3.error ~ LEN + I(LEN^2) + vowel + JA + LP + LD + 
##     TCX + TCY + TTX + TTY + TBX + TBY + hyoidX + hyoidY + (LEN:vowel) + 
##     (I(LEN^2):vowel) + (JA:vowel) + (LP:vowel) + (LD:vowel) + 
##     (TCX:vowel) + (TCY:vowel) + (TTX:vowel) + (TTY:vowel) + (TBX:vowel) + 
##     (TBY:vowel) + (hyoidX:vowel) + (hyoidY:vowel) + (JA:LEN) + 
##     (LP:LEN) + (LD:LEN) + (TCX:LEN) + (TCY:LEN) + (TTX:LEN) + 
##     (TTY:LEN) + (TBX:LEN) + (TBY:LEN) + (hyoidX:LEN) + (hyoidY:LEN) + 
##     replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.84774 -0.11208  0.00065  0.10732  2.32284 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       1.342e+01  1.462e+00   9.179  < 2e-16 ***
## LEN               3.378e+00  3.935e-01   8.583  < 2e-16 ***
## I(LEN^2)          1.892e-01  3.049e-02   6.203 6.31e-10 ***
## vowela            8.941e+00  1.987e+00   4.499 7.08e-06 ***
## vowelae          -4.960e+00  2.046e+00  -2.425 0.015387 *  
## voweli            3.215e+00  1.993e+00   1.613 0.106926    
## vowelu            4.543e+00  1.761e+00   2.580 0.009917 ** 
## JA               -2.223e-01  3.501e-02  -6.349 2.51e-10 ***
## LP                5.766e-01  1.197e-01   4.817 1.53e-06 ***
## LD               -2.357e-01  6.099e-02  -3.865 0.000113 ***
## TCX              -8.906e-01  1.342e-01  -6.638 3.77e-11 ***
## TCY              -8.002e-01  1.987e-01  -4.028 5.78e-05 ***
## TTX              -4.907e-01  7.939e-02  -6.181 7.28e-10 ***
## TTY               7.123e-01  7.920e-02   8.994  < 2e-16 ***
## TBX               2.080e-01  5.626e-02   3.697 0.000222 ***
## TBY               1.354e-01  9.256e-02   1.463 0.143586    
## hyoidX            2.701e-01  1.661e-01   1.626 0.103967    
## hyoidY            5.852e-01  2.986e-01   1.959 0.050159 .  
## replication      -1.501e-05  1.982e-04  -0.076 0.939652    
## generation       -9.507e-05  6.851e-05  -1.388 0.165347    
## LEN:vowela        2.616e+00  4.875e-01   5.367 8.64e-08 ***
## LEN:vowelae      -1.732e+00  5.040e-01  -3.436 0.000598 ***
## LEN:voweli        5.783e-01  5.159e-01   1.121 0.262348    
## LEN:vowelu        1.070e+00  4.451e-01   2.405 0.016237 *  
## I(LEN^2):vowela   2.097e-01  3.050e-02   6.875 7.56e-12 ***
## I(LEN^2):vowelae -1.138e-01  3.192e-02  -3.564 0.000371 ***
## I(LEN^2):voweli   8.829e-03  3.326e-02   0.265 0.790692    
## I(LEN^2):vowelu   9.883e-02  2.910e-02   3.397 0.000692 ***
## vowela:JA         2.010e-02  1.688e-02   1.191 0.233755    
## vowelae:JA        1.324e-02  2.334e-02   0.567 0.570441    
## voweli:JA         4.933e-03  1.396e-02   0.353 0.723744    
## vowelu:JA         2.168e-02  1.146e-02   1.892 0.058566 .  
## vowela:LP        -2.917e-02  5.034e-02  -0.580 0.562280    
## vowelae:LP       -4.712e-02  5.876e-02  -0.802 0.422706    
## voweli:LP        -5.008e-02  4.361e-02  -1.148 0.250875    
## vowelu:LP        -2.048e-01  4.262e-02  -4.805 1.62e-06 ***
## vowela:LD         4.082e-02  2.428e-02   1.682 0.092764 .  
## vowelae:LD        2.790e-02  2.634e-02   1.059 0.289627    
## voweli:LD         1.729e-02  2.009e-02   0.860 0.389662    
## vowelu:LD         7.616e-02  2.364e-02   3.221 0.001290 ** 
## vowela:TCX        2.266e+00  1.711e-01  13.248  < 2e-16 ***
## vowelae:TCX      -2.280e-01  9.097e-02  -2.506 0.012263 *  
## voweli:TCX       -1.203e-01  6.166e-02  -1.950 0.051239 .  
## vowelu:TCX        3.028e-01  8.157e-02   3.712 0.000209 ***
## vowela:TCY        1.216e+00  1.111e-01  10.951  < 2e-16 ***
## vowelae:TCY       2.790e-02  7.620e-02   0.366 0.714265    
## voweli:TCY        1.535e-01  6.907e-02   2.223 0.026325 *  
## vowelu:TCY       -2.165e-01  6.102e-02  -3.547 0.000395 ***
## vowela:TTX       -7.237e-02  2.906e-02  -2.490 0.012831 *  
## vowelae:TTX      -4.279e-02  2.808e-02  -1.524 0.127673    
## voweli:TTX        4.446e-02  2.418e-02   1.839 0.066083 .  
## vowelu:TTX        7.106e-02  2.706e-02   2.626 0.008686 ** 
## vowela:TTY        1.661e-01  3.069e-02   5.413 6.68e-08 ***
## vowelae:TTY      -3.634e-02  4.304e-02  -0.844 0.398519    
## voweli:TTY       -3.419e-02  2.636e-02  -1.297 0.194594    
## vowelu:TTY       -2.263e-01  2.313e-02  -9.783  < 2e-16 ***
## vowela:TBX        2.722e-02  1.682e-02   1.618 0.105684    
## vowelae:TBX      -1.304e-02  2.730e-02  -0.478 0.632999    
## voweli:TBX       -3.109e-02  2.659e-02  -1.169 0.242321    
## vowelu:TBX       -5.251e-02  1.922e-02  -2.731 0.006344 ** 
## vowela:TBY        3.372e-02  2.914e-02   1.157 0.247282    
## vowelae:TBY      -3.626e-02  5.064e-02  -0.716 0.473983    
## voweli:TBY        2.742e-02  4.887e-02   0.561 0.574836    
## vowelu:TBY       -4.695e-02  2.933e-02  -1.601 0.109466    
## vowela:hyoidX     4.563e-01  6.864e-02   6.648 3.54e-11 ***
## vowelae:hyoidX    6.696e-02  6.565e-02   1.020 0.307863    
## voweli:hyoidX    -3.029e-01  6.109e-02  -4.957 7.55e-07 ***
## vowelu:hyoidX     1.205e-02  5.039e-02   0.239 0.811062    
## vowela:hyoidY    -9.053e-01  1.084e-01  -8.350  < 2e-16 ***
## vowelae:hyoidY    3.019e-01  1.082e-01   2.791 0.005282 ** 
## voweli:hyoidY    -5.077e-02  9.929e-02  -0.511 0.609123    
## vowelu:hyoidY     5.230e-01  8.811e-02   5.936 3.27e-09 ***
## LEN:JA           -3.115e-02  4.420e-03  -7.046 2.28e-12 ***
## LEN:LP            7.140e-02  1.526e-02   4.679 3.01e-06 ***
## LEN:LD           -2.849e-02  7.516e-03  -3.791 0.000153 ***
## LEN:TCX          -1.470e-01  1.593e-02  -9.232  < 2e-16 ***
## LEN:TCY          -1.088e-01  2.440e-02  -4.459 8.56e-06 ***
## LEN:TTX          -5.819e-02  9.410e-03  -6.184 7.12e-10 ***
## LEN:TTY           8.613e-02  9.335e-03   9.227  < 2e-16 ***
## LEN:TBX           2.956e-02  6.631e-03   4.458 8.58e-06 ***
## LEN:TBY           1.866e-02  1.077e-02   1.732 0.083343 .  
## LEN:hyoidX        2.266e-02  2.020e-02   1.122 0.261985    
## LEN:hyoidY        1.271e-01  3.374e-02   3.768 0.000168 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3109 on 2917 degrees of freedom
## Multiple R-squared:  0.7658, Adjusted R-squared:  0.7592 
## F-statistic: 116.3 on 82 and 2917 DF,  p-value: < 2.2e-16

F4

##                  Df Sum Sq Mean Sq  F value   Pr(>F)    
## LEN               1  65.88   65.88 1791.539  < 2e-16 ***
## I(LEN^2)          1   0.56    0.56   15.106 0.000104 ***
## vowel             4 164.02   41.00 1115.022  < 2e-16 ***
## JA                1   0.11    0.11    2.890 0.089254 .  
## LP                1   2.20    2.20   59.761 1.46e-14 ***
## LD                1   0.86    0.86   23.394 1.39e-06 ***
## TCX               1   3.53    3.53   95.997  < 2e-16 ***
## TCY               1   0.01    0.01    0.161 0.688707    
## TTX               1   1.97    1.97   53.472 3.37e-13 ***
## TTY               1  18.06   18.06  491.131  < 2e-16 ***
## TBX               1   0.62    0.62   16.795 4.28e-05 ***
## TBY               1   0.44    0.44   12.094 0.000513 ***
## hyoidX            1   0.00    0.00    0.003 0.958270    
## hyoidY            1   4.74    4.74  128.795  < 2e-16 ***
## replication       1   0.04    0.04    1.108 0.292539    
## generation        1   2.65    2.65   71.968  < 2e-16 ***
## LEN:vowel         4  11.13    2.78   75.632  < 2e-16 ***
## I(LEN^2):vowel    4  17.95    4.49  122.055  < 2e-16 ***
## vowel:JA          4   2.41    0.60   16.365 2.89e-13 ***
## vowel:LP          4   2.61    0.65   17.753 2.08e-14 ***
## vowel:LD          4   0.96    0.24    6.558 2.99e-05 ***
## vowel:TCX         4  12.28    3.07   83.460  < 2e-16 ***
## vowel:TCY         4   8.49    2.12   57.717  < 2e-16 ***
## vowel:TTX         4   0.68    0.17    4.610 0.001036 ** 
## vowel:TTY         4   2.18    0.54   14.795 5.69e-12 ***
## vowel:TBX         4   0.14    0.03    0.951 0.433485    
## vowel:TBY         4   0.39    0.10    2.632 0.032648 *  
## vowel:hyoidX      4   7.84    1.96   53.282  < 2e-16 ***
## vowel:hyoidY      4   7.18    1.79   48.790  < 2e-16 ***
## LEN:JA            1   1.14    1.14   31.066 2.72e-08 ***
## LEN:LP            1   1.49    1.49   40.420 2.37e-10 ***
## LEN:LD            1   0.70    0.70   19.131 1.26e-05 ***
## LEN:TCX           1   0.00    0.00    0.004 0.948325    
## LEN:TCY           1   6.65    6.65  180.727  < 2e-16 ***
## LEN:TTX           1   0.33    0.33    8.845 0.002964 ** 
## LEN:TTY           1  27.26   27.26  741.186  < 2e-16 ***
## LEN:TBX           1   2.77    2.77   75.254  < 2e-16 ***
## LEN:TBY           1   0.02    0.02    0.508 0.476025    
## LEN:hyoidX        1   0.22    0.22    5.924 0.014998 *  
## LEN:hyoidY        1   0.22    0.22    5.973 0.014589 *  
## Residuals      2917 107.27    0.04                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f4.m0)
## 
## $vowel
##                 diff          lwr         upr     p adj
## a-schwa  -0.18706467 -0.217284443 -0.15684489 0.0000000
## ae-schwa  0.03495083  0.004731057  0.06517061 0.0139374
## i-schwa   0.50373283  0.473513057  0.53395261 0.0000000
## u-schwa  -0.04582850 -0.076048276 -0.01560872 0.0003453
## ae-a      0.22201550  0.191795724  0.25223528 0.0000000
## i-a       0.69079750  0.660577724  0.72101728 0.0000000
## u-a       0.14123617  0.111016391  0.17145594 0.0000000
## i-ae      0.46878200  0.438562224  0.49900178 0.0000000
## u-ae     -0.08077933 -0.110999109 -0.05055956 0.0000000
## u-i      -0.54956133 -0.579781109 -0.51934156 0.0000000
## 
## Call:
## lm(formula = F4 ~ LEN + I(LEN^2) + vowel + JA + LP + LD + TCX + 
##     TCY + TTX + TTY + TBX + TBY + hyoidX + hyoidY + (LEN:vowel) + 
##     (I(LEN^2):vowel) + (JA:vowel) + (LP:vowel) + (LD:vowel) + 
##     (TCX:vowel) + (TCY:vowel) + (TTX:vowel) + (TTY:vowel) + (TBX:vowel) + 
##     (TBY:vowel) + (hyoidX:vowel) + (hyoidY:vowel) + (JA:LEN) + 
##     (LP:LEN) + (LD:LEN) + (TCX:LEN) + (TCY:LEN) + (TTX:LEN) + 
##     (TTY:LEN) + (TBX:LEN) + (TBY:LEN) + (hyoidX:LEN) + (hyoidY:LEN) + 
##     replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.95512 -0.08366 -0.00757  0.07324  1.39072 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       1.906e+01  9.018e-01  21.141  < 2e-16 ***
## LEN               8.888e-01  2.428e-01   3.661 0.000255 ***
## I(LEN^2)          5.937e-02  1.881e-02   3.156 0.001614 ** 
## vowela           -2.547e+00  1.226e+00  -2.077 0.037851 *  
## vowelae          -8.083e-01  1.262e+00  -0.641 0.521889    
## voweli            1.361e+00  1.230e+00   1.107 0.268490    
## vowelu            1.230e+01  1.086e+00  11.329  < 2e-16 ***
## JA                8.062e-02  2.160e-02   3.732 0.000193 ***
## LP               -5.549e-01  7.385e-02  -7.515 7.54e-14 ***
## LD                1.907e-01  3.763e-02   5.068 4.28e-07 ***
## TCX               1.295e-01  8.277e-02   1.565 0.117728    
## TCY              -1.522e+00  1.226e-01 -12.419  < 2e-16 ***
## TTX              -1.655e-01  4.897e-02  -3.380 0.000734 ***
## TTY              -1.286e+00  4.886e-02 -26.320  < 2e-16 ***
## TBX              -1.976e-01  3.470e-02  -5.695 1.36e-08 ***
## TBY               1.070e-01  5.710e-02   1.874 0.061047 .  
## hyoidX            1.614e-01  1.025e-01   1.575 0.115373    
## hyoidY            2.966e-01  1.842e-01   1.610 0.107460    
## replication      -6.552e-05  1.223e-04  -0.536 0.592153    
## generation        1.788e-05  4.226e-05   0.423 0.672248    
## LEN:vowela       -5.429e-01  3.007e-01  -1.805 0.071142 .  
## LEN:vowelae      -3.827e-01  3.109e-01  -1.231 0.218504    
## LEN:voweli       -3.709e-02  3.182e-01  -0.117 0.907233    
## LEN:vowelu        2.960e+00  2.746e-01  10.780  < 2e-16 ***
## I(LEN^2):vowela  -3.358e-02  1.881e-02  -1.785 0.074348 .  
## I(LEN^2):vowelae -2.481e-02  1.969e-02  -1.260 0.207821    
## I(LEN^2):voweli  -1.485e-02  2.052e-02  -0.724 0.469216    
## I(LEN^2):vowelu   1.660e-01  1.795e-02   9.247  < 2e-16 ***
## vowela:JA         1.714e-03  1.041e-02   0.165 0.869255    
## vowelae:JA       -1.775e-02  1.440e-02  -1.233 0.217663    
## voweli:JA        -4.185e-02  8.609e-03  -4.861 1.23e-06 ***
## vowelu:JA         4.229e-04  7.070e-03   0.060 0.952300    
## vowela:LP         1.775e-02  3.105e-02   0.572 0.567569    
## vowelae:LP       -2.092e-02  3.625e-02  -0.577 0.563978    
## voweli:LP        -5.569e-02  2.690e-02  -2.070 0.038526 *  
## vowelu:LP        -1.783e-01  2.629e-02  -6.782 1.43e-11 ***
## vowela:LD         1.907e-02  1.498e-02   1.273 0.202957    
## vowelae:LD        5.142e-03  1.625e-02   0.316 0.751685    
## voweli:LD         4.927e-02  1.239e-02   3.975 7.21e-05 ***
## vowelu:LD         6.070e-02  1.458e-02   4.162 3.25e-05 ***
## vowela:TCX        5.906e-01  1.055e-01   5.596 2.40e-08 ***
## vowelae:TCX      -8.784e-02  5.612e-02  -1.565 0.117621    
## voweli:TCX       -1.275e-01  3.804e-02  -3.352 0.000813 ***
## vowelu:TCX       -2.111e-01  5.032e-02  -4.195 2.81e-05 ***
## vowela:TCY        4.691e-01  6.852e-02   6.846 9.20e-12 ***
## vowelae:TCY       7.942e-02  4.701e-02   1.690 0.091219 .  
## voweli:TCY        1.805e-01  4.261e-02   4.235 2.35e-05 ***
## vowelu:TCY        2.911e-01  3.765e-02   7.733 1.44e-14 ***
## vowela:TTX        5.675e-02  1.793e-02   3.165 0.001565 ** 
## vowelae:TTX       5.468e-02  1.732e-02   3.157 0.001612 ** 
## voweli:TTX        6.450e-02  1.492e-02   4.323 1.59e-05 ***
## vowelu:TTX        2.763e-02  1.669e-02   1.655 0.097964 .  
## vowela:TTY        2.683e-02  1.893e-02   1.418 0.156433    
## vowelae:TTY       9.159e-02  2.655e-02   3.449 0.000570 ***
## voweli:TTY        1.121e-02  1.626e-02   0.689 0.490740    
## vowelu:TTY       -6.984e-02  1.427e-02  -4.895 1.04e-06 ***
## vowela:TBX       -2.383e-02  1.037e-02  -2.297 0.021713 *  
## vowelae:TBX      -1.023e-02  1.684e-02  -0.607 0.543586    
## voweli:TBX       -2.957e-02  1.640e-02  -1.803 0.071461 .  
## vowelu:TBX       -5.075e-02  1.186e-02  -4.279 1.94e-05 ***
## vowela:TBY       -3.125e-02  1.798e-02  -1.738 0.082247 .  
## vowelae:TBY      -8.472e-02  3.124e-02  -2.712 0.006728 ** 
## voweli:TBY        3.612e-02  3.015e-02   1.198 0.230953    
## vowelu:TBY       -7.242e-02  1.809e-02  -4.003 6.41e-05 ***
## vowela:hyoidX     3.448e-01  4.234e-02   8.145 5.58e-16 ***
## vowelae:hyoidX    9.403e-02  4.050e-02   2.322 0.020306 *  
## voweli:hyoidX    -2.135e-01  3.769e-02  -5.665 1.61e-08 ***
## vowelu:hyoidX    -7.277e-02  3.109e-02  -2.341 0.019299 *  
## vowela:hyoidY    -4.503e-01  6.689e-02  -6.732 2.01e-11 ***
## vowelae:hyoidY    1.205e-01  6.672e-02   1.806 0.071053 .  
## voweli:hyoidY     1.752e-01  6.125e-02   2.860 0.004260 ** 
## vowelu:hyoidY    -1.653e-01  5.436e-02  -3.040 0.002384 ** 
## LEN:JA            1.043e-02  2.727e-03   3.825 0.000133 ***
## LEN:LP           -7.433e-02  9.414e-03  -7.896 4.03e-15 ***
## LEN:LD            2.553e-02  4.637e-03   5.507 3.98e-08 ***
## LEN:TCX           3.939e-03  9.825e-03   0.401 0.688533    
## LEN:TCY          -1.912e-01  1.505e-02 -12.702  < 2e-16 ***
## LEN:TTX          -1.389e-02  5.805e-03  -2.392 0.016810 *  
## LEN:TTY          -1.546e-01  5.759e-03 -26.850  < 2e-16 ***
## LEN:TBX          -3.025e-02  4.090e-03  -7.395 1.84e-13 ***
## LEN:TBY           4.891e-03  6.645e-03   0.736 0.461785    
## LEN:hyoidX        2.256e-02  1.246e-02   1.810 0.070345 .  
## LEN:hyoidY        5.086e-02  2.081e-02   2.444 0.014589 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1918 on 2917 degrees of freedom
## Multiple R-squared:  0.7802, Adjusted R-squared:  0.774 
## F-statistic: 126.2 on 82 and 2917 DF,  p-value: < 2.2e-16
##                  Df Sum Sq Mean Sq F value   Pr(>F)    
## LEN               1   0.11   0.114   1.920 0.165948    
## I(LEN^2)          1   6.12   6.125 103.256  < 2e-16 ***
## vowel             4  23.65   5.912  99.667  < 2e-16 ***
## JA                1   0.78   0.783  13.198 0.000285 ***
## LP                1   1.73   1.733  29.222 6.98e-08 ***
## LD                1   0.05   0.054   0.905 0.341442    
## TCX               1   5.60   5.604  94.485  < 2e-16 ***
## TCY               1   0.92   0.923  15.564 8.16e-05 ***
## TTX               1   0.03   0.034   0.572 0.449431    
## TTY               1  27.30  27.302 460.277  < 2e-16 ***
## TBX               1   1.39   1.390  23.431 1.36e-06 ***
## TBY               1   0.23   0.234   3.947 0.047047 *  
## hyoidX            1   1.23   1.230  20.736 5.49e-06 ***
## hyoidY            1   0.12   0.117   1.979 0.159630    
## replication       1   0.00   0.002   0.033 0.856053    
## generation        1   7.55   7.545 127.202  < 2e-16 ***
## LEN:vowel         4  10.17   2.542  42.853  < 2e-16 ***
## I(LEN^2):vowel    4  10.60   2.651  44.695  < 2e-16 ***
## vowel:JA          4   2.02   0.504   8.496 8.19e-07 ***
## vowel:LP          4   2.67   0.666  11.234 4.80e-09 ***
## vowel:LD          4   0.46   0.115   1.937 0.101557    
## vowel:TCX         4   8.98   2.245  37.845  < 2e-16 ***
## vowel:TCY         4   1.91   0.478   8.051 1.88e-06 ***
## vowel:TTX         4   0.23   0.058   0.979 0.417585    
## vowel:TTY         4   6.86   1.716  28.928  < 2e-16 ***
## vowel:TBX         4   0.49   0.123   2.073 0.081720 .  
## vowel:TBY         4   1.58   0.394   6.640 2.57e-05 ***
## vowel:hyoidX      4   3.03   0.758  12.773 2.62e-10 ***
## vowel:hyoidY      4   0.21   0.052   0.873 0.479373    
## LEN:JA            1   1.96   1.962  33.076 9.78e-09 ***
## LEN:LP            1   2.80   2.801  47.217 7.74e-12 ***
## LEN:LD            1   2.39   2.394  40.368 2.43e-10 ***
## LEN:TCX           1   0.03   0.032   0.547 0.459528    
## LEN:TCY           1   0.64   0.637  10.731 0.001066 ** 
## LEN:TTX           1   0.00   0.005   0.078 0.780510    
## LEN:TTY           1  23.02  23.016 388.016  < 2e-16 ***
## LEN:TBX           1   0.00   0.001   0.024 0.875771    
## LEN:TBY           1   0.80   0.805  13.566 0.000234 ***
## LEN:hyoidX        1   0.26   0.258   4.357 0.036946 *  
## LEN:hyoidY        1   1.61   1.608  27.102 2.06e-07 ***
## Residuals      2917 173.02   0.059                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f4e.m0)
## 
## $vowel
##                 diff         lwr         upr     p adj
## a-schwa   0.07531938  0.03693935 0.113699402 0.0000009
## ae-schwa  0.08824385  0.04986383 0.126623878 0.0000000
## i-schwa   0.05149025  0.01311022 0.089870274 0.0023666
## u-schwa   0.26251898  0.22413895 0.300899006 0.0000000
## ae-a      0.01292448 -0.02545555 0.051304501 0.8896131
## i-a      -0.02382913 -0.06220915 0.014550898 0.4373629
## u-a       0.18719960  0.14881958 0.225579630 0.0000000
## i-ae     -0.03675360 -0.07513363 0.001626422 0.0681041
## u-ae      0.17427513  0.13589510 0.212655155 0.0000000
## u-i       0.21102873  0.17264871 0.249408758 0.0000000
## 
## Call:
## lm(formula = F4.error ~ LEN + I(LEN^2) + vowel + JA + LP + LD + 
##     TCX + TCY + TTX + TTY + TBX + TBY + hyoidX + hyoidY + (LEN:vowel) + 
##     (I(LEN^2):vowel) + (JA:vowel) + (LP:vowel) + (LD:vowel) + 
##     (TCX:vowel) + (TCY:vowel) + (TTX:vowel) + (TTY:vowel) + (TBX:vowel) + 
##     (TBY:vowel) + (hyoidX:vowel) + (hyoidY:vowel) + (JA:LEN) + 
##     (LP:LEN) + (LD:LEN) + (TCX:LEN) + (TCY:LEN) + (TTX:LEN) + 
##     (TTY:LEN) + (TBX:LEN) + (TBY:LEN) + (hyoidX:LEN) + (hyoidY:LEN) + 
##     replication + generation, data = d)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.1781 -0.0789 -0.0103  0.0589  3.9665 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       9.053e+00  1.145e+00   7.905 3.78e-15 ***
## LEN               1.728e+00  3.083e-01   5.606 2.27e-08 ***
## I(LEN^2)          8.209e-02  2.389e-02   3.436 0.000598 ***
## vowela            9.448e-01  1.557e+00   0.607 0.543982    
## vowelae          -1.761e+00  1.603e+00  -1.099 0.272037    
## voweli           -2.652e+00  1.562e+00  -1.698 0.089636 .  
## vowelu            1.073e+01  1.379e+00   7.779 1.00e-14 ***
## JA                6.182e-02  2.743e-02   2.254 0.024291 *  
## LP               -7.815e-01  9.379e-02  -8.332  < 2e-16 ***
## LD                3.293e-01  4.779e-02   6.890 6.79e-12 ***
## TCX              -2.269e-01  1.051e-01  -2.159 0.030948 *  
## TCY              -3.723e-01  1.557e-01  -2.392 0.016842 *  
## TTX              -2.478e-01  6.220e-02  -3.985 6.93e-05 ***
## TTY              -1.273e+00  6.205e-02 -20.516  < 2e-16 ***
## TBX              -1.054e-01  4.408e-02  -2.390 0.016889 *  
## TBY              -2.659e-01  7.252e-02  -3.667 0.000249 ***
## hyoidX           -4.413e-01  1.301e-01  -3.391 0.000705 ***
## hyoidY            1.217e+00  2.340e-01   5.200 2.13e-07 ***
## replication      -1.329e-04  1.553e-04  -0.855 0.392393    
## generation       -2.835e-04  5.368e-05  -5.282 1.37e-07 ***
## LEN:vowela        3.378e-01  3.819e-01   0.884 0.376539    
## LEN:vowelae      -8.968e-02  3.949e-01  -0.227 0.820355    
## LEN:voweli       -7.193e-01  4.042e-01  -1.780 0.075207 .  
## LEN:vowelu        2.401e+00  3.487e-01   6.885 7.03e-12 ***
## I(LEN^2):vowela   2.747e-02  2.389e-02   1.150 0.250343    
## I(LEN^2):vowelae  6.036e-03  2.501e-02   0.241 0.809302    
## I(LEN^2):voweli  -6.685e-02  2.606e-02  -2.565 0.010361 *  
## I(LEN^2):vowelu   1.232e-01  2.280e-02   5.406 6.97e-08 ***
## vowela:JA         7.338e-04  1.322e-02   0.055 0.955752    
## vowelae:JA       -6.064e-03  1.828e-02  -0.332 0.740190    
## voweli:JA        -1.494e-02  1.093e-02  -1.366 0.171903    
## vowelu:JA         1.640e-02  8.979e-03   1.827 0.067798 .  
## vowela:LP         4.146e-02  3.944e-02   1.051 0.293232    
## vowelae:LP        2.827e-02  4.604e-02   0.614 0.539151    
## voweli:LP        -6.228e-02  3.417e-02  -1.823 0.068413 .  
## vowelu:LP        -1.825e-01  3.339e-02  -5.467 4.96e-08 ***
## vowela:LD        -1.346e-02  1.902e-02  -0.708 0.479130    
## vowelae:LD        2.976e-03  2.064e-02   0.144 0.885355    
## voweli:LD         2.341e-02  1.574e-02   1.487 0.137043    
## vowelu:LD         3.352e-02  1.852e-02   1.809 0.070489 .  
## vowela:TCX       -2.691e-01  1.340e-01  -2.008 0.044754 *  
## vowelae:TCX       4.533e-02  7.127e-02   0.636 0.524837    
## voweli:TCX       -3.484e-02  4.831e-02  -0.721 0.470795    
## vowelu:TCX       -2.890e-02  6.391e-02  -0.452 0.651101    
## vowela:TCY       -2.409e-01  8.702e-02  -2.768 0.005673 ** 
## vowelae:TCY      -7.413e-02  5.970e-02  -1.242 0.214424    
## voweli:TCY       -1.007e-02  5.411e-02  -0.186 0.852461    
## vowelu:TCY        7.357e-02  4.781e-02   1.539 0.123973    
## vowela:TTX       -3.850e-02  2.277e-02  -1.691 0.091028 .  
## vowelae:TTX      -2.128e-02  2.200e-02  -0.967 0.333588    
## voweli:TTX        1.353e-02  1.895e-02   0.714 0.475289    
## vowelu:TTX       -3.915e-02  2.120e-02  -1.847 0.064901 .  
## vowela:TTY       -4.438e-02  2.404e-02  -1.846 0.065025 .  
## vowelae:TTY       1.099e-01  3.372e-02   3.258 0.001135 ** 
## voweli:TTY        4.186e-02  2.065e-02   2.027 0.042732 *  
## vowelu:TTY       -1.248e-01  1.812e-02  -6.884 7.08e-12 ***
## vowela:TBX       -1.651e-02  1.318e-02  -1.253 0.210425    
## vowelae:TBX       2.441e-02  2.139e-02   1.141 0.253915    
## voweli:TBX        6.608e-02  2.083e-02   3.172 0.001529 ** 
## vowelu:TBX       -2.961e-02  1.506e-02  -1.966 0.049418 *  
## vowela:TBY        2.021e-02  2.283e-02   0.885 0.376177    
## vowelae:TBY       5.717e-02  3.967e-02   1.441 0.149724    
## voweli:TBY        1.673e-01  3.829e-02   4.369 1.29e-05 ***
## vowelu:TBY       -4.521e-02  2.298e-02  -1.968 0.049191 *  
## vowela:hyoidX     9.741e-02  5.377e-02   1.811 0.070168 .  
## vowelae:hyoidX   -6.940e-02  5.143e-02  -1.349 0.177353    
## voweli:hyoidX    -2.655e-02  4.786e-02  -0.555 0.579143    
## vowelu:hyoidX    -8.818e-02  3.948e-02  -2.233 0.025593 *  
## vowela:hyoidY     9.378e-02  8.495e-02   1.104 0.269696    
## vowelae:hyoidY   -1.186e-01  8.474e-02  -1.400 0.161642    
## voweli:hyoidY    -1.481e-01  7.779e-02  -1.904 0.056957 .  
## vowelu:hyoidY    -2.163e-01  6.903e-02  -3.133 0.001750 ** 
## LEN:JA            9.209e-03  3.463e-03   2.659 0.007871 ** 
## LEN:LP           -1.003e-01  1.196e-02  -8.390  < 2e-16 ***
## LEN:LD            4.069e-02  5.889e-03   6.909 5.95e-12 ***
## LEN:TCX          -2.986e-02  1.248e-02  -2.393 0.016764 *  
## LEN:TCY          -5.172e-02  1.911e-02  -2.706 0.006848 ** 
## LEN:TTX          -3.296e-02  7.373e-03  -4.470 8.11e-06 ***
## LEN:TTY          -1.513e-01  7.314e-03 -20.688  < 2e-16 ***
## LEN:TBX          -1.217e-02  5.195e-03  -2.343 0.019198 *  
## LEN:TBY          -3.446e-02  8.440e-03  -4.083 4.57e-05 ***
## LEN:hyoidX       -5.100e-02  1.582e-02  -3.223 0.001284 ** 
## LEN:hyoidY        1.376e-01  2.643e-02   5.206 2.06e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2435 on 2917 degrees of freedom
## Multiple R-squared:  0.4798, Adjusted R-squared:  0.4651 
## F-statistic:  32.8 on 82 and 2917 DF,  p-value: < 2.2e-16

F5

##                  Df Sum Sq Mean Sq  F value   Pr(>F)    
## LEN               1  65.93   65.93 2054.018  < 2e-16 ***
## I(LEN^2)          1  77.15   77.15 2403.542  < 2e-16 ***
## vowel             4 106.48   26.62  829.339  < 2e-16 ***
## JA                1   0.54    0.54   16.687 4.53e-05 ***
## LP                1   4.03    4.03  125.603  < 2e-16 ***
## LD                1   1.73    1.73   53.986 2.61e-13 ***
## TCX               1   4.49    4.49  139.743  < 2e-16 ***
## TCY               1   1.17    1.17   36.296 1.91e-09 ***
## TTX               1   0.00    0.00    0.038 0.845622    
## TTY               1   8.07    8.07  251.288  < 2e-16 ***
## TBX               1   0.47    0.47   14.732 0.000127 ***
## TBY               1   0.61    0.61   18.914 1.41e-05 ***
## hyoidX            1   0.11    0.11    3.450 0.063342 .  
## hyoidY            1   0.07    0.07    2.258 0.132998    
## replication       1   0.05    0.05    1.572 0.210074    
## generation        1   3.04    3.04   94.859  < 2e-16 ***
## LEN:vowel         4  23.10    5.77  179.887  < 2e-16 ***
## I(LEN^2):vowel    4  78.80   19.70  613.784  < 2e-16 ***
## vowel:JA          4   0.97    0.24    7.557 4.71e-06 ***
## vowel:LP          4   1.04    0.26    8.108 1.69e-06 ***
## vowel:LD          4   1.64    0.41   12.770 2.64e-10 ***
## vowel:TCX         4   4.90    1.23   38.166  < 2e-16 ***
## vowel:TCY         4   1.49    0.37   11.624 2.30e-09 ***
## vowel:TTX         4   0.70    0.17    5.416 0.000242 ***
## vowel:TTY         4   7.15    1.79   55.726  < 2e-16 ***
## vowel:TBX         4   0.18    0.04    1.371 0.241265    
## vowel:TBY         4   1.03    0.26    8.014 2.01e-06 ***
## vowel:hyoidX      4   0.17    0.04    1.303 0.266630    
## vowel:hyoidY      4   1.04    0.26    8.118 1.66e-06 ***
## LEN:JA            1   1.22    1.22   38.031 7.92e-10 ***
## LEN:LP            1   0.20    0.20    6.303 0.012110 *  
## LEN:LD            1   0.40    0.40   12.609 0.000390 ***
## LEN:TCX           1   0.15    0.15    4.617 0.031738 *  
## LEN:TCY           1   0.80    0.80   24.881 6.46e-07 ***
## LEN:TTX           1   0.44    0.44   13.627 0.000227 ***
## LEN:TTY           1   0.93    0.93   28.920 8.14e-08 ***
## LEN:TBX           1   0.32    0.32    9.895 0.001674 ** 
## LEN:TBY           1   0.02    0.02    0.613 0.433566    
## LEN:hyoidX        1   0.22    0.22    6.934 0.008503 ** 
## LEN:hyoidY        1   0.71    0.71   22.050 2.78e-06 ***
## Residuals      2917  93.63    0.03                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f5.m0)
## 
## $vowel
##                 diff          lwr          upr     p adj
## a-schwa   0.02494017 -0.003292715  0.053173049 0.1125456
## ae-schwa  0.09895817  0.070725285  0.127191049 0.0000000
## i-schwa  -0.03595900 -0.064191882 -0.007726118 0.0046859
## u-schwa  -0.43585017 -0.464083049 -0.407617285 0.0000000
## ae-a      0.07401800  0.045785118  0.102250882 0.0000000
## i-a      -0.06089917 -0.089132049 -0.032666285 0.0000000
## u-a      -0.46079033 -0.489023215 -0.432557451 0.0000000
## i-ae     -0.13491717 -0.163150049 -0.106684285 0.0000000
## u-ae     -0.53480833 -0.563041215 -0.506575451 0.0000000
## u-i      -0.39989117 -0.428124049 -0.371658285 0.0000000
## 
## Call:
## lm(formula = F5 ~ LEN + I(LEN^2) + vowel + JA + LP + LD + TCX + 
##     TCY + TTX + TTY + TBX + TBY + hyoidX + hyoidY + (LEN:vowel) + 
##     (I(LEN^2):vowel) + (JA:vowel) + (LP:vowel) + (LD:vowel) + 
##     (TCX:vowel) + (TCY:vowel) + (TTX:vowel) + (TTY:vowel) + (TBX:vowel) + 
##     (TBY:vowel) + (hyoidX:vowel) + (hyoidY:vowel) + (JA:LEN) + 
##     (LP:LEN) + (LD:LEN) + (TCX:LEN) + (TCY:LEN) + (TTX:LEN) + 
##     (TTY:LEN) + (TBX:LEN) + (TBY:LEN) + (hyoidX:LEN) + (hyoidY:LEN) + 
##     replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.05127 -0.07931  0.00146  0.07900  1.45999 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       2.578e+01  8.425e-01  30.597  < 2e-16 ***
## LEN               2.404e+00  2.268e-01  10.601  < 2e-16 ***
## I(LEN^2)          1.803e-01  1.757e-02  10.259  < 2e-16 ***
## vowela            5.508e+00  1.145e+00   4.810 1.59e-06 ***
## vowelae           3.170e+00  1.179e+00   2.689 0.007213 ** 
## voweli           -3.854e+00  1.149e+00  -3.355 0.000805 ***
## vowelu            3.041e+01  1.015e+00  29.969  < 2e-16 ***
## JA                8.592e-02  2.018e-02   4.258 2.13e-05 ***
## LP               -2.818e-01  6.899e-02  -4.084 4.55e-05 ***
## LD                1.500e-01  3.515e-02   4.267 2.04e-05 ***
## TCX               3.081e-01  7.733e-02   3.985 6.92e-05 ***
## TCY              -3.431e-01  1.145e-01  -2.996 0.002756 ** 
## TTX               1.315e-01  4.575e-02   2.874 0.004086 ** 
## TTY              -2.349e-01  4.564e-02  -5.146 2.84e-07 ***
## TBX              -9.478e-02  3.242e-02  -2.923 0.003491 ** 
## TBY              -6.303e-02  5.335e-02  -1.182 0.237496    
## hyoidX           -1.642e-01  9.573e-02  -1.716 0.086319 .  
## hyoidY           -6.865e-01  1.721e-01  -3.988 6.81e-05 ***
## replication      -6.378e-05  1.142e-04  -0.558 0.576700    
## generation       -1.632e-04  3.949e-05  -4.132 3.69e-05 ***
## LEN:vowela        1.255e+00  2.810e-01   4.465 8.30e-06 ***
## LEN:vowelae       6.407e-01  2.905e-01   2.206 0.027478 *  
## LEN:voweli       -1.218e+00  2.973e-01  -4.096 4.33e-05 ***
## LEN:vowelu        7.672e+00  2.565e-01  29.908  < 2e-16 ***
## I(LEN^2):vowela   6.707e-02  1.758e-02   3.816 0.000139 ***
## I(LEN^2):vowelae  2.976e-02  1.840e-02   1.618 0.105802    
## I(LEN^2):voweli  -7.564e-02  1.917e-02  -3.946 8.14e-05 ***
## I(LEN^2):vowelu   4.609e-01  1.677e-02  27.481  < 2e-16 ***
## vowela:JA         3.462e-02  9.727e-03   3.559 0.000378 ***
## vowelae:JA        1.972e-02  1.345e-02   1.466 0.142693    
## voweli:JA         1.277e-02  8.043e-03   1.588 0.112494    
## vowelu:JA         2.964e-02  6.605e-03   4.487 7.49e-06 ***
## vowela:LP         5.869e-02  2.901e-02   2.023 0.043167 *  
## vowelae:LP        1.045e-01  3.387e-02   3.086 0.002045 ** 
## voweli:LP        -2.606e-02  2.513e-02  -1.037 0.299798    
## vowelu:LP        -3.859e-02  2.456e-02  -1.571 0.116284    
## vowela:LD        -4.183e-02  1.399e-02  -2.990 0.002818 ** 
## vowelae:LD       -5.206e-02  1.518e-02  -3.430 0.000613 ***
## voweli:LD         1.155e-02  1.158e-02   0.997 0.318655    
## vowelu:LD         1.862e-02  1.363e-02   1.367 0.171839    
## vowela:TCX       -4.777e-01  9.860e-02  -4.845 1.33e-06 ***
## vowelae:TCX      -2.205e-02  5.243e-02  -0.421 0.674070    
## voweli:TCX       -1.213e-01  3.554e-02  -3.414 0.000648 ***
## vowelu:TCX        2.438e-01  4.701e-02   5.186 2.29e-07 ***
## vowela:TCY       -4.075e-01  6.401e-02  -6.366 2.25e-10 ***
## vowelae:TCY      -8.812e-02  4.392e-02  -2.007 0.044895 *  
## voweli:TCY       -2.381e-02  3.981e-02  -0.598 0.549858    
## vowelu:TCY       -1.020e-01  3.517e-02  -2.899 0.003768 ** 
## vowela:TTX        1.960e-02  1.675e-02   1.170 0.241986    
## vowelae:TTX       3.234e-02  1.618e-02   1.999 0.045751 *  
## voweli:TTX       -7.062e-03  1.394e-02  -0.507 0.612452    
## vowelu:TTX       -2.815e-02  1.560e-02  -1.805 0.071198 .  
## vowela:TTY       -5.012e-02  1.769e-02  -2.834 0.004627 ** 
## vowelae:TTY      -7.758e-02  2.481e-02  -3.128 0.001780 ** 
## voweli:TTY        6.987e-02  1.519e-02   4.599 4.42e-06 ***
## vowelu:TTY       -1.184e-01  1.333e-02  -8.883  < 2e-16 ***
## vowela:TBX       -3.706e-03  9.692e-03  -0.382 0.702249    
## vowelae:TBX      -1.478e-02  1.573e-02  -0.939 0.347711    
## voweli:TBX        4.212e-03  1.532e-02   0.275 0.783441    
## vowelu:TBX       -2.038e-02  1.108e-02  -1.840 0.065933 .  
## vowela:TBY        2.228e-02  1.680e-02   1.326 0.184810    
## vowelae:TBY      -7.191e-02  2.918e-02  -2.464 0.013797 *  
## voweli:TBY       -7.859e-03  2.816e-02  -0.279 0.780222    
## vowelu:TBY       -6.983e-03  1.690e-02  -0.413 0.679528    
## vowela:hyoidX    -4.706e-02  3.956e-02  -1.190 0.234231    
## vowelae:hyoidX    1.808e-02  3.784e-02   0.478 0.632859    
## voweli:hyoidX     5.479e-02  3.521e-02   1.556 0.119791    
## vowelu:hyoidX    -4.183e-02  2.904e-02  -1.440 0.149844    
## vowela:hyoidY     2.233e-01  6.249e-02   3.574 0.000357 ***
## vowelae:hyoidY    2.964e-02  6.233e-02   0.475 0.634469    
## voweli:hyoidY     1.720e-01  5.722e-02   3.006 0.002672 ** 
## vowelu:hyoidY    -1.451e-01  5.078e-02  -2.857 0.004313 ** 
## LEN:JA            1.340e-02  2.547e-03   5.261 1.54e-07 ***
## LEN:LP           -3.142e-02  8.795e-03  -3.573 0.000359 ***
## LEN:LD            1.714e-02  4.332e-03   3.956 7.81e-05 ***
## LEN:TCX           3.039e-02  9.179e-03   3.311 0.000939 ***
## LEN:TCY          -4.348e-02  1.406e-02  -3.092 0.002004 ** 
## LEN:TTX           1.575e-02  5.423e-03   2.904 0.003716 ** 
## LEN:TTY          -2.525e-02  5.380e-03  -4.694 2.80e-06 ***
## LEN:TBX          -1.127e-02  3.821e-03  -2.950 0.003199 ** 
## LEN:TBY          -4.337e-03  6.208e-03  -0.699 0.484860    
## LEN:hyoidX       -1.734e-02  1.164e-02  -1.489 0.136517    
## LEN:hyoidY       -9.130e-02  1.944e-02  -4.696 2.78e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1792 on 2917 degrees of freedom
## Multiple R-squared:  0.8109, Adjusted R-squared:  0.8056 
## F-statistic: 152.6 on 82 and 2917 DF,  p-value: < 2.2e-16
##                  Df Sum Sq Mean Sq  F value   Pr(>F)    
## LEN               1   78.9   78.94  976.906  < 2e-16 ***
## I(LEN^2)          1  162.8  162.76 2014.139  < 2e-16 ***
## vowel             4  363.9   90.98 1125.888  < 2e-16 ***
## JA                1    0.1    0.13    1.548 0.213604    
## LP                1    9.4    9.42  116.544  < 2e-16 ***
## LD                1    9.1    9.15  113.183  < 2e-16 ***
## TCX               1   53.4   53.37  660.518  < 2e-16 ***
## TCY               1    1.6    1.59   19.631 9.74e-06 ***
## TTX               1    0.4    0.36    4.456 0.034860 *  
## TTY               1   10.4   10.36  128.214  < 2e-16 ***
## TBX               1    0.5    0.48    5.977 0.014550 *  
## TBY               1    0.1    0.08    0.957 0.328062    
## hyoidX            1    0.0    0.04    0.488 0.484772    
## hyoidY            1    1.4    1.39   17.216 3.43e-05 ***
## replication       1    0.1    0.12    1.527 0.216650    
## generation        1    7.3    7.28   90.101  < 2e-16 ***
## LEN:vowel         4  145.6   36.41  450.606  < 2e-16 ***
## I(LEN^2):vowel    4  306.6   76.65  948.558  < 2e-16 ***
## vowel:JA          4    2.0    0.50    6.206 5.70e-05 ***
## vowel:LP          4    0.1    0.02    0.222 0.926166    
## vowel:LD          4    1.2    0.29    3.650 0.005688 ** 
## vowel:TCX         4    2.9    0.73    9.087 2.71e-07 ***
## vowel:TCY         4    0.8    0.21    2.594 0.034774 *  
## vowel:TTX         4    0.7    0.17    2.117 0.076135 .  
## vowel:TTY         4    7.5    1.86   23.051  < 2e-16 ***
## vowel:TBX         4    0.2    0.06    0.722 0.576634    
## vowel:TBY         4    0.4    0.10    1.261 0.282992    
## vowel:hyoidX      4    0.2    0.06    0.766 0.547311    
## vowel:hyoidY      4    2.4    0.60    7.469 5.55e-06 ***
## LEN:JA            1    7.1    7.05   87.293  < 2e-16 ***
## LEN:LP            1    1.1    1.07   13.228 0.000281 ***
## LEN:LD            1    1.7    1.71   21.196 4.32e-06 ***
## LEN:TCX           1    0.8    0.75    9.317 0.002290 ** 
## LEN:TCY           1    1.3    1.29   16.008 6.46e-05 ***
## LEN:TTX           1    0.0    0.03    0.364 0.546261    
## LEN:TTY           1    3.3    3.34   41.374 1.46e-10 ***
## LEN:TBX           1    0.9    0.95   11.732 0.000623 ***
## LEN:TBY           1    0.1    0.08    1.012 0.314616    
## LEN:hyoidX        1    0.9    0.93   11.520 0.000698 ***
## LEN:hyoidY        1    1.7    1.67   20.668 5.68e-06 ***
## Residuals      2917  235.7    0.08                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f5e.m0)
## 
## $vowel
##                 diff          lwr        upr     p adj
## a-schwa  0.017963483 -0.026833057 0.06276002 0.8094568
## ae-schwa 0.023620836 -0.021175704 0.06841738 0.6022372
## i-schwa  0.050998397  0.006201857 0.09579494 0.0163306
## u-schwa  0.892911019  0.848114480 0.93770756 0.0000000
## ae-a     0.005657353 -0.039139187 0.05045389 0.9969712
## i-a      0.033034914 -0.011761626 0.07783145 0.2599542
## u-a      0.874947537  0.830150997 0.91974408 0.0000000
## i-ae     0.027377561 -0.017418978 0.07217410 0.4539795
## u-ae     0.869290184  0.824493644 0.91408672 0.0000000
## u-i      0.841912622  0.797116083 0.88670916 0.0000000
## 
## Call:
## lm(formula = F5.error ~ LEN + I(LEN^2) + vowel + JA + LP + LD + 
##     TCX + TCY + TTX + TTY + TBX + TBY + hyoidX + hyoidY + (LEN:vowel) + 
##     (I(LEN^2):vowel) + (JA:vowel) + (LP:vowel) + (LD:vowel) + 
##     (TCX:vowel) + (TCY:vowel) + (TTX:vowel) + (TTY:vowel) + (TBX:vowel) + 
##     (TBY:vowel) + (hyoidX:vowel) + (hyoidY:vowel) + (JA:LEN) + 
##     (LP:LEN) + (LD:LEN) + (TCX:LEN) + (TCY:LEN) + (TTX:LEN) + 
##     (TTY:LEN) + (TBX:LEN) + (TBY:LEN) + (hyoidX:LEN) + (hyoidY:LEN) + 
##     replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.61749 -0.06507 -0.00064  0.06227  2.43263 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       8.109e+00  1.337e+00   6.066 1.48e-09 ***
## LEN               1.437e+00  3.599e-01   3.993 6.69e-05 ***
## I(LEN^2)          5.897e-02  2.788e-02   2.115 0.034516 *  
## vowela            5.965e+00  1.817e+00   3.282 0.001041 ** 
## vowelae           2.101e+00  1.871e+00   1.123 0.261544    
## voweli           -2.602e+00  1.823e+00  -1.427 0.153642    
## vowelu            6.391e+01  1.610e+00  39.696  < 2e-16 ***
## JA                1.993e-01  3.202e-02   6.224 5.52e-10 ***
## LP               -5.411e-01  1.095e-01  -4.943 8.12e-07 ***
## LD                2.912e-01  5.578e-02   5.220 1.91e-07 ***
## TCX               3.943e-01  1.227e-01   3.214 0.001325 ** 
## TCY              -6.932e-01  1.817e-01  -3.815 0.000139 ***
## TTX              -1.040e-01  7.260e-02  -1.432 0.152269    
## TTY              -5.124e-01  7.242e-02  -7.075 1.86e-12 ***
## TBX              -1.463e-01  5.144e-02  -2.843 0.004498 ** 
## TBY               4.217e-02  8.464e-02   0.498 0.618388    
## hyoidX           -7.123e-01  1.519e-01  -4.690 2.86e-06 ***
## hyoidY            1.247e+00  2.731e-01   4.565 5.21e-06 ***
## replication      -1.905e-04  1.813e-04  -1.051 0.293418    
## generation       -2.758e-04  6.265e-05  -4.401 1.11e-05 ***
## LEN:vowela        1.441e+00  4.458e-01   3.232 0.001244 ** 
## LEN:vowelae       6.877e-01  4.609e-01   1.492 0.135785    
## LEN:voweli       -8.896e-01  4.717e-01  -1.886 0.059433 .  
## LEN:vowelu        1.516e+01  4.070e-01  37.242  < 2e-16 ***
## I(LEN^2):vowela   8.646e-02  2.789e-02   3.100 0.001954 ** 
## I(LEN^2):vowelae  4.316e-02  2.919e-02   1.479 0.139326    
## I(LEN^2):voweli  -5.943e-02  3.042e-02  -1.954 0.050811 .  
## I(LEN^2):vowelu   9.164e-01  2.661e-02  34.441  < 2e-16 ***
## vowela:JA         1.485e-02  1.543e-02   0.962 0.336129    
## vowelae:JA        9.012e-03  2.134e-02   0.422 0.672852    
## voweli:JA         2.645e-02  1.276e-02   2.073 0.038306 *  
## vowelu:JA         4.964e-02  1.048e-02   4.737 2.28e-06 ***
## vowela:LP         4.850e-02  4.603e-02   1.054 0.292107    
## vowelae:LP        3.053e-02  5.373e-02   0.568 0.569965    
## voweli:LP        -3.838e-02  3.988e-02  -0.962 0.335889    
## vowelu:LP        -5.438e-02  3.897e-02  -1.395 0.162977    
## vowela:LD        -2.479e-02  2.220e-02  -1.117 0.264271    
## vowelae:LD       -9.278e-03  2.409e-02  -0.385 0.700108    
## voweli:LD         2.323e-02  1.837e-02   1.264 0.206181    
## vowelu:LD         8.844e-02  2.162e-02   4.091 4.42e-05 ***
## vowela:TCX       -3.298e-01  1.564e-01  -2.108 0.035124 *  
## vowelae:TCX       3.404e-02  8.319e-02   0.409 0.682457    
## voweli:TCX       -8.329e-02  5.639e-02  -1.477 0.139758    
## vowelu:TCX        4.263e-01  7.459e-02   5.715 1.21e-08 ***
## vowela:TCY       -2.896e-01  1.016e-01  -2.852 0.004379 ** 
## vowelae:TCY       1.870e-02  6.968e-02   0.268 0.788437    
## voweli:TCY       -2.145e-03  6.316e-02  -0.034 0.972906    
## vowelu:TCY       -2.155e-01  5.580e-02  -3.862 0.000115 ***
## vowela:TTX       -2.609e-02  2.658e-02  -0.982 0.326343    
## vowelae:TTX      -5.453e-03  2.568e-02  -0.212 0.831857    
## voweli:TTX       -4.162e-03  2.212e-02  -0.188 0.850756    
## vowelu:TTX       -5.131e-02  2.475e-02  -2.073 0.038221 *  
## vowela:TTY       -4.584e-02  2.806e-02  -1.634 0.102434    
## vowelae:TTY       2.793e-02  3.936e-02   0.710 0.477925    
## voweli:TTY        4.043e-02  2.410e-02   1.677 0.093554 .  
## vowelu:TTY       -1.329e-01  2.115e-02  -6.283 3.81e-10 ***
## vowela:TBX       -1.901e-02  1.538e-02  -1.236 0.216599    
## vowelae:TBX       9.129e-03  2.496e-02   0.366 0.714644    
## voweli:TBX        1.609e-02  2.431e-02   0.662 0.508176    
## vowelu:TBX       -4.008e-02  1.758e-02  -2.280 0.022674 *  
## vowela:TBY       -1.432e-02  2.665e-02  -0.537 0.591011    
## vowelae:TBY       4.714e-03  4.631e-02   0.102 0.918931    
## voweli:TBY       -1.087e-02  4.469e-02  -0.243 0.807771    
## vowelu:TBY       -3.968e-02  2.682e-02  -1.480 0.139087    
## vowela:hyoidX    -5.740e-02  6.276e-02  -0.915 0.360517    
## vowelae:hyoidX    2.122e-02  6.003e-02   0.354 0.723737    
## voweli:hyoidX     1.703e-01  5.587e-02   3.048 0.002327 ** 
## vowelu:hyoidX    -4.285e-02  4.608e-02  -0.930 0.352500    
## vowela:hyoidY     1.877e-01  9.915e-02   1.893 0.058456 .  
## vowelae:hyoidY   -1.307e-01  9.890e-02  -1.321 0.186509    
## voweli:hyoidY     1.118e-01  9.079e-02   1.232 0.218120    
## vowelu:hyoidY     2.544e-01  8.057e-02   3.158 0.001606 ** 
## LEN:JA            2.870e-02  4.042e-03   7.100 1.56e-12 ***
## LEN:LP           -6.737e-02  1.395e-02  -4.828 1.45e-06 ***
## LEN:LD            3.677e-02  6.873e-03   5.350 9.49e-08 ***
## LEN:TCX           4.063e-02  1.456e-02   2.790 0.005311 ** 
## LEN:TCY          -8.681e-02  2.231e-02  -3.891 0.000102 ***
## LEN:TTX          -1.410e-02  8.605e-03  -1.639 0.101331    
## LEN:TTY          -6.020e-02  8.537e-03  -7.052 2.19e-12 ***
## LEN:TBX          -1.912e-02  6.063e-03  -3.153 0.001634 ** 
## LEN:TBY           5.331e-03  9.851e-03   0.541 0.588414    
## LEN:hyoidX       -8.023e-02  1.847e-02  -4.344 1.45e-05 ***
## LEN:hyoidY        1.403e-01  3.085e-02   4.546 5.68e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2843 on 2917 degrees of freedom
## Multiple R-squared:  0.8346, Adjusted R-squared:  0.8299 
## F-statistic: 179.4 on 82 and 2917 DF,  p-value: < 2.2e-16
Summary of F1–F5 regressions with betas (for non-factor DVs and ‘.’ for factors), p-values, and adjusted R2. Interactions are denoted by ‘:’.
DVs, interactions & R2 F1 F1.err F2 F2.err F3 F3.err F4 F4.err F5 F5.err
LEN -0.48 (1.3e-05***) 0.13 (0.28) 0.13 (0.4) 1.2 (3.2e-11***) -3.1 (3.8e-22***) 3.4 (1.5e-17***) 0.89 (0.00026***) 1.7 (2.3e-08***) 2.4 (8.7e-26***) 1.4 (6.7e-05***)
LEN^2 -0.036 (2e-05***) -0.0013 (0.89) 0.0087 (0.46) 0.1 (2.1e-12***) -0.2 (2.9e-16***) 0.19 (6.3e-10***) 0.059 (0.0016**) 0.082 (0.0006***) 0.18 (2.8e-24***) 0.059 (0.035*)
vowel . (0***) . (6.9e-114***) . (0***) . (0***) . (0***) . (1.2e-142***) . (0***) . (1.3e-79***) . (0***) . (0***)
JA -0.0096 (0.33) 0.016 (0.14) 0.018 (0.18) 0.068 (4.7e-05***) 0.13 (2.7e-06***) -0.22 (2.5e-10***) 0.081 (0.00019***) 0.062 (0.024*) 0.086 (2.1e-05***) 0.2 (5.5e-10***)
LP -0.11 (0.00099***) -0.28 (1.7e-13***) -0.27 (2.8e-09***) -0.25 (1.4e-05***) -0.65 (1.4e-11***) 0.58 (1.5e-06***) -0.55 (7.5e-14***) -0.78 (1.2e-16***) -0.28 (4.5e-05***) -0.54 (8.1e-07***)
LD 0.057 (0.00091***) 0.056 (0.0029**) 0.047 (0.045*) 0.1 (0.00033***) 0.24 (8.2e-07***) -0.24 (0.00011***) 0.19 (4.3e-07***) 0.33 (6.8e-12***) 0.15 (2e-05***) 0.29 (1.9e-07***)
TCX -0.15 (5.5e-05***) -0.033 (0.42) 0.4 (2.2e-14***) -0.54 (4.1e-17***) 0.51 (1.9e-06***) -0.89 (3.8e-11***) 0.13 (0.12) -0.23 (0.031*) 0.31 (6.9e-05***) 0.39 (0.0013**)
TCY 0.36 (6.2e-11***) -0.0069 (0.91) -0.22 (0.0038**) -1.4 (9.4e-46***) 0.48 (0.0026**) -0.8 (5.8e-05***) -1.5 (1.5e-34***) -0.37 (0.017*) -0.34 (0.0028**) -0.69 (0.00014***)
TTX 0.051 (0.021*) 0.09 (0.00027***) 0.17 (2.9e-08***) -0.063 (0.094) 0.23 (0.00031***) -0.49 (7.3e-10***) -0.17 (0.00073***) -0.25 (6.9e-05***) 0.13 (0.0041**) -0.1 (0.15)
TTY -0.025 (0.26) -0.13 (3.6e-07***) 0.0049 (0.87) -0.12 (0.0013**) -0.94 (5.2e-48***) 0.71 (4.2e-19***) -1.3 (3.6e-137***) -1.3 (1.7e-87***) -0.23 (2.8e-07***) -0.51 (1.9e-12***)
TBX -0.054 (0.0006***) -0.012 (0.48) -0.0097 (0.65) 0.066 (0.014*) -0.15 (0.00084***) 0.21 (0.00022***) -0.2 (1.4e-08***) -0.11 (0.017*) -0.095 (0.0035**) -0.15 (0.0045**)
TBY -0.036 (0.17) 0.092 (0.0014**) -0.042 (0.24) -0.02 (0.65) -0.42 (1.1e-08***) 0.14 (0.14) 0.11 (0.061) -0.27 (0.00025***) -0.063 (0.24) 0.042 (0.62)
hyoidX -0.11 (0.022*) -0.077 (0.13) -0.12 (0.052) 0.26 (0.00084***) 0.063 (0.63) 0.27 (0.1) 0.16 (0.12) -0.44 (0.00071***) -0.16 (0.086) -0.71 (2.9e-06***)
hyoidY 0.088 (0.29) 0.43 (4.7e-06***) 0.28 (0.016*) -0.14 (0.31) 0.093 (0.7) 0.59 (0.05) 0.3 (0.11) 1.2 (2.1e-07***) -0.69 (6.8e-05***) 1.2 (5.2e-06***)
replication 2.6e-05 (0.64) 6.1e-05 (0.32) 0.00011 (0.17) -0.00015 (0.12) 3.1e-05 (0.84) -1.5e-05 (0.94) -6.6e-05 (0.59) -0.00013 (0.39) -6.4e-05 (0.58) -0.00019 (0.29)
generation -0.00014 (1.6e-13***) -0.00015 (1.6e-12***) -6.4e-05 (0.016*) -0.0002 (9.3e-10***) -4.1e-05 (0.45) -9.5e-05 (0.17) 1.8e-05 (0.67) -0.00028 (1.4e-07***) -0.00016 (3.7e-05***) -0.00028 (1.1e-05***)
LEN:vowel . (4.4e-141***) . (4.5e-162***) . (0***) . (0***) . (1.1e-53***) . (1.4e-181***) . (4.3e-61***) . (5.6e-35***) . (6.4e-138***) . (9.8e-303***)
LEN^2:vowel . (1.3e-160***) . (2.1e-32***) . (6.1e-311***) . (0***) . (8.4e-85***) . (1.1e-62***) . (2e-96***) . (1.8e-36***) . (0***) . (0***)
vowel:JA . (3.5e-44***) . (5.6e-18***) . (3.8e-18***) . (2.5e-07***) . (1.3e-09***) . (8.9e-09***) . (2.9e-13***) . (8.2e-07***) . (4.7e-06***) . (5.7e-05***)
vowel:LP . (5.4e-54***) . (1.1e-25***) . (1.8e-05***) . (0.029*) . (0.004**) . (2.7e-09***) . (2.1e-14***) . (4.8e-09***) . (1.7e-06***) . (0.93)
vowel:LD . (4.4e-22***) . (5.6e-08***) . (6.2e-14***) . (0.042*) . (0.00013***) . (6.8e-07***) . (3e-05***) . (0.1) . (2.6e-10***) . (0.0057**)
vowel:TCX . (2.2e-74***) . (1e-106***) . (5.9e-42***) . (1.7e-38***) . (7.5e-06***) . (5.1e-11***) . (3.5e-67***) . (6.5e-31***) . (3.6e-31***) . (2.7e-07***)
vowel:TCY . (5.5e-18***) . (1e-08***) . (1.5e-46***) . (2.5e-40***) . (1.2e-59***) . (2.3e-23***) . (6.1e-47***) . (1.9e-06***) . (2.3e-09***) . (0.035*)
vowel:TTX . (2.1e-36***) . (6.5e-18***) . (0.069) . (0.1) . (0.27) . (0.063) . (0.001**) . (0.42) . (0.00024***) . (0.076)
vowel:TTY . (1.2e-06***) . (0.0042**) . (3e-13***) . (0.5) . (1.4e-05***) . (6.4e-30***) . (5.7e-12***) . (1.3e-23***) . (2.4e-45***) . (8.9e-19***)
vowel:TBX . (3.7e-48***) . (0.0016**) . (4.1e-06***) . (0.056) . (0.048*) . (0.0044**) . (0.43) . (0.082) . (0.24) . (0.58)
vowel:TBY . (6.4e-55***) . (1.5e-07***) . (0.025*) . (7.7e-05***) . (3.9e-05***) . (0.00033***) . (0.033*) . (2.6e-05***) . (2e-06***) . (0.28)
vowel:hyoidX . (3.4e-26***) . (0.016*) . (1.7e-09***) . (1.4e-12***) . (0.00069***) . (0.01**) . (2.2e-43***) . (2.6e-10***) . (0.27) . (0.55)
vowel:hyoidY . (3.7e-29***) . (1.2e-21***) . (8.3e-11***) . (5e-13***) . (1.3e-54***) . (4.3e-38***) . (8.8e-40***) . (0.48) . (1.7e-06***) . (5.5e-06***)
LEN:JA -0.00074 (0.55) 0.0028 (0.045*) 0.0023 (0.17) 0.0093 (1e-05***) 0.019 (1.2e-07***) -0.031 (2.3e-12***) 0.01 (0.00013***) 0.0092 (0.0079**) 0.013 (1.5e-07***) 0.029 (1.6e-12***)
LEN:LP -0.015 (0.00053***) -0.036 (4.6e-14***) -0.037 (3.1e-10***) -0.034 (3e-06***) -0.08 (5.9e-11***) 0.071 (3e-06***) -0.074 (4e-15***) -0.1 (7.4e-17***) -0.031 (0.00036***) -0.067 (1.5e-06***)
LEN:LD 0.0067 (0.0015**) 0.0069 (0.0033**) 0.0065 (0.025*) 0.014 (9.7e-05***) 0.028 (2.6e-06***) -0.028 (0.00015***) 0.026 (4e-08***) 0.041 (6e-12***) 0.017 (7.8e-05***) 0.037 (9.5e-08***)
LEN:TCX -0.017 (0.00013***) -0.0051 (0.3) 0.044 (8.6e-13***) -0.08 (2.1e-25***) 0.1 (4.1e-15***) -0.15 (4.9e-20***) 0.0039 (0.69) -0.03 (0.017*) 0.03 (0.00094***) 0.041 (0.0053**)
LEN:TCY 0.046 (2e-11***) -0.001 (0.9) -0.026 (0.0049**) -0.18 (1.2e-49***) 0.061 (0.0018**) -0.11 (8.6e-06***) -0.19 (5.1e-36***) -0.052 (0.0068**) -0.043 (0.002**) -0.087 (0.0001***)
LEN:TTX 0.0068 (0.0098**) 0.011 (0.00018***) 0.022 (2.8e-09***) -0.0074 (0.1) 0.024 (0.0015**) -0.058 (7.1e-10***) -0.014 (0.017*) -0.033 (8.1e-06***) 0.016 (0.0037**) -0.014 (0.1)
LEN:TTY -0.0024 (0.35) -0.014 (1.3e-06***) -0.00046 (0.9) -0.017 (0.00015***) -0.11 (2.2e-51***) 0.086 (5.2e-20***) -0.15 (4.2e-142***) -0.15 (7.9e-89***) -0.025 (2.8e-06***) -0.06 (2.2e-12***)
LEN:TBX -0.0068 (0.00025***) -0.0023 (0.27) -0.0018 (0.49) 0.0067 (0.034*) -0.022 (4.6e-05***) 0.03 (8.6e-06***) -0.03 (1.8e-13***) -0.012 (0.019*) -0.011 (0.0032**) -0.019 (0.0016**)
LEN:TBY -0.0031 (0.3) 0.011 (0.001**) -0.0071 (0.087) -0.0063 (0.22) -0.054 (2.5e-10***) 0.019 (0.083) 0.0049 (0.46) -0.034 (4.6e-05***) -0.0043 (0.48) 0.0053 (0.59)
LEN:hyoidX -0.011 (0.051) -0.0073 (0.25) -0.013 (0.096) 0.037 (0.00013***) 0.015 (0.35) 0.023 (0.26) 0.023 (0.07) -0.051 (0.0013**) -0.017 (0.14) -0.08 (1.4e-05***)
LEN:hyoidY 0.011 (0.26) 0.049 (3.3e-06***) 0.03 (0.021*) -0.0098 (0.54) -0.028 (0.3) 0.13 (0.00017***) 0.051 (0.015*) 0.14 (2.1e-07***) -0.091 (2.8e-06***) 0.14 (5.7e-06***)
adjusted R2 99.7% 56.1% 99.8% 79.9% 82.1% 75.9% 77.4% 46.5% 80.6% 83.0%

Overall acoustic error over F1 – F5 on LEN

## Analysis of Variance Table
## 
## Response: acoustic.err
##                  Df Sum Sq Mean Sq    F value    Pr(>F)    
## LEN               1  86.28   86.28  3501.8440 < 2.2e-16 ***
## I(LEN^2)          1 360.11  360.11 14616.6775 < 2.2e-16 ***
## vowel             4 255.48   63.87  2592.3885 < 2.2e-16 ***
## JA                1   3.16    3.16   128.3440 < 2.2e-16 ***
## LP                1   6.38    6.38   258.9087 < 2.2e-16 ***
## LD                1   1.11    1.11    45.2422 2.087e-11 ***
## TCX               1  24.86   24.86  1008.8877 < 2.2e-16 ***
## TCY               1   2.37    2.37    96.3430 < 2.2e-16 ***
## TTX               1   0.27    0.27    10.8473 0.0010012 ** 
## TTY               1  26.84   26.84  1089.2217 < 2.2e-16 ***
## TBX               1   8.27    8.27   335.7895 < 2.2e-16 ***
## TBY               1   1.74    1.74    70.5182 < 2.2e-16 ***
## hyoidX            1   0.31    0.31    12.6493 0.0003817 ***
## hyoidY            1   0.04    0.04     1.5303 0.2161611    
## replication       1   0.01    0.01     0.3646 0.5460084    
## generation        1  12.08   12.08   490.3345 < 2.2e-16 ***
## LEN:vowel         4  43.53   10.88   441.7516 < 2.2e-16 ***
## I(LEN^2):vowel    4  31.06    7.76   315.1445 < 2.2e-16 ***
## vowel:JA          4   5.38    1.35    54.6385 < 2.2e-16 ***
## vowel:LP          4   2.92    0.73    29.6634 < 2.2e-16 ***
## vowel:LD          4   2.33    0.58    23.6435 < 2.2e-16 ***
## vowel:TCX         4   4.20    1.05    42.6061 < 2.2e-16 ***
## vowel:TCY         4   2.94    0.73    29.8282 < 2.2e-16 ***
## vowel:TTX         4   0.21    0.05     2.1590 0.0711484 .  
## vowel:TTY         4  10.73    2.68   108.8559 < 2.2e-16 ***
## vowel:TBX         4   1.47    0.37    14.9219 4.472e-12 ***
## vowel:TBY         4   3.37    0.84    34.1585 < 2.2e-16 ***
## vowel:hyoidX      4   6.90    1.73    70.0492 < 2.2e-16 ***
## vowel:hyoidY      4  10.39    2.60   105.3832 < 2.2e-16 ***
## LEN:JA            1   0.96    0.96    39.1642 4.468e-10 ***
## LEN:LP            1   0.83    0.83    33.7004 7.121e-09 ***
## LEN:LD            1   1.86    1.86    75.3329 < 2.2e-16 ***
## LEN:TCX           1   4.37    4.37   177.4931 < 2.2e-16 ***
## LEN:TCY           1   3.55    3.55   144.1932 < 2.2e-16 ***
## LEN:TTX           1   0.37    0.37    14.9498 0.0001128 ***
## LEN:TTY           1   1.39    1.39    56.4490 7.624e-14 ***
## LEN:TBX           1   0.03    0.03     1.1627 0.2809907    
## LEN:TBY           1   0.02    0.02     0.8232 0.3643292    
## LEN:hyoidX        1   0.03    0.03     1.0627 0.3026959    
## LEN:hyoidY        1   0.20    0.20     7.9772 0.0047693 ** 
## Residuals      2917  71.87    0.02                         
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = err.m0)
## 
## $vowel
##                 diff          lwr         upr     p adj
## a-schwa   0.31471076  0.289975562  0.33944597 0.0000000
## ae-schwa  0.17299662  0.148261421  0.19773183 0.0000000
## i-schwa   0.34905558  0.324320380  0.37379079 0.0000000
## u-schwa   0.87065452  0.845919314  0.89538972 0.0000000
## ae-a     -0.14171414 -0.166449343 -0.11697894 0.0000000
## i-a       0.03434482  0.009609616  0.05908002 0.0014455
## u-a       0.55594375  0.531208550  0.58067896 0.0000000
## i-ae      0.17605896  0.151323757  0.20079416 0.0000000
## u-ae      0.69765789  0.672922691  0.72239310 0.0000000
## u-i       0.52159893  0.496863732  0.54633414 0.0000000
## 
## Call:
## lm(formula = acoustic.err ~ LEN + I(LEN^2) + vowel + JA + LP + 
##     LD + TCX + TCY + TTX + TTY + TBX + TBY + hyoidX + hyoidY + 
##     (LEN:vowel) + (I(LEN^2):vowel) + (JA:vowel) + (LP:vowel) + 
##     (LD:vowel) + (TCX:vowel) + (TCY:vowel) + (TTX:vowel) + (TTY:vowel) + 
##     (TBX:vowel) + (TBY:vowel) + (hyoidX:vowel) + (hyoidY:vowel) + 
##     (JA:LEN) + (LP:LEN) + (LD:LEN) + (TCX:LEN) + (TCY:LEN) + 
##     (TTX:LEN) + (TTY:LEN) + (TBX:LEN) + (TBY:LEN) + (hyoidX:LEN) + 
##     (hyoidY:LEN) + replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.87009 -0.09479 -0.00760  0.08748  0.92780 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       2.285e+01  7.381e-01  30.960  < 2e-16 ***
## LEN               6.199e+00  1.987e-01  31.199  < 2e-16 ***
## I(LEN^2)          3.981e-01  1.540e-02  25.855  < 2e-16 ***
## vowela            9.983e-01  1.003e+00   0.995 0.319861    
## vowelae          -5.683e+00  1.033e+00  -5.502 4.08e-08 ***
## voweli            7.802e+00  1.007e+00   7.751 1.25e-14 ***
## vowelu            2.278e+01  8.890e-01  25.625  < 2e-16 ***
## JA                2.800e-02  1.768e-02   1.584 0.113335    
## LP               -3.971e-01  6.045e-02  -6.569 5.96e-11 ***
## LD                2.047e-01  3.080e-02   6.648 3.53e-11 ***
## TCX              -3.770e-01  6.775e-02  -5.566 2.85e-08 ***
## TCY              -1.204e+00  1.003e-01 -11.998  < 2e-16 ***
## TTX              -2.168e-01  4.009e-02  -5.408 6.90e-08 ***
## TTY              -3.465e-01  3.999e-02  -8.664  < 2e-16 ***
## TBX              -1.003e-02  2.841e-02  -0.353 0.723926    
## TBY               1.569e-02  4.674e-02   0.336 0.737063    
## hyoidX           -1.136e-01  8.387e-02  -1.354 0.175847    
## hyoidY            2.732e-02  1.508e-01   0.181 0.856243    
## replication      -1.560e-04  1.001e-04  -1.558 0.119239    
## generation       -4.187e-04  3.459e-05 -12.102  < 2e-16 ***
## LEN:vowela        3.177e-01  2.462e-01   1.290 0.196987    
## LEN:vowelae      -1.531e+00  2.545e-01  -6.017 1.99e-09 ***
## LEN:voweli        1.726e+00  2.605e-01   6.625 4.12e-11 ***
## LEN:vowelu        4.843e+00  2.247e-01  21.550  < 2e-16 ***
## I(LEN^2):vowela   4.377e-02  1.540e-02   2.843 0.004507 ** 
## I(LEN^2):vowelae -9.150e-02  1.612e-02  -5.677 1.50e-08 ***
## I(LEN^2):voweli   9.140e-02  1.680e-02   5.442 5.71e-08 ***
## I(LEN^2):vowelu   2.922e-01  1.469e-02  19.887  < 2e-16 ***
## vowela:JA         1.505e-02  8.522e-03   1.766 0.077476 .  
## vowelae:JA       -2.593e-02  1.178e-02  -2.200 0.027875 *  
## voweli:JA         8.182e-03  7.047e-03   1.161 0.245697    
## vowelu:JA         2.856e-02  5.787e-03   4.936 8.42e-07 ***
## vowela:LP         2.576e-02  2.542e-02   1.013 0.310971    
## vowelae:LP        1.045e-02  2.967e-02   0.352 0.724709    
## voweli:LP        -1.211e-01  2.202e-02  -5.500 4.12e-08 ***
## vowelu:LP        -2.146e-01  2.152e-02  -9.973  < 2e-16 ***
## vowela:LD         3.623e-03  1.226e-02   0.296 0.767604    
## vowelae:LD        1.993e-02  1.330e-02   1.499 0.134026    
## voweli:LD         4.782e-02  1.014e-02   4.714 2.54e-06 ***
## vowelu:LD         9.480e-02  1.194e-02   7.941 2.83e-15 ***
## vowela:TCX        5.729e-01  8.638e-02   6.632 3.92e-11 ***
## vowelae:TCX      -2.145e-01  4.593e-02  -4.669 3.16e-06 ***
## voweli:TCX       -3.527e-01  3.113e-02 -11.328  < 2e-16 ***
## vowelu:TCX       -8.068e-02  4.119e-02  -1.959 0.050201 .  
## vowela:TCY        5.048e-01  5.608e-02   9.000  < 2e-16 ***
## vowelae:TCY      -1.128e-01  3.848e-02  -2.931 0.003408 ** 
## voweli:TCY        1.116e-01  3.488e-02   3.199 0.001392 ** 
## vowelu:TCY       -2.271e-01  3.081e-02  -7.370 2.22e-13 ***
## vowela:TTX       -2.158e-02  1.468e-02  -1.471 0.141514    
## vowelae:TTX       1.142e-02  1.418e-02   0.805 0.420838    
## voweli:TTX        2.715e-02  1.221e-02   2.223 0.026299 *  
## vowelu:TTX        4.350e-02  1.366e-02   3.183 0.001471 ** 
## vowela:TTY        7.552e-02  1.549e-02   4.874 1.15e-06 ***
## vowelae:TTY       1.587e-01  2.173e-02   7.301 3.66e-13 ***
## voweli:TTY        4.946e-02  1.331e-02   3.717 0.000206 ***
## vowelu:TTY       -1.387e-01  1.168e-02 -11.875  < 2e-16 ***
## vowela:TBX        3.475e-02  8.492e-03   4.092 4.38e-05 ***
## vowelae:TBX       3.043e-02  1.378e-02   2.207 0.027374 *  
## voweli:TBX        5.282e-02  1.342e-02   3.935 8.52e-05 ***
## vowelu:TBX       -1.113e-02  9.707e-03  -1.147 0.251554    
## vowela:TBY        1.301e-01  1.472e-02   8.838  < 2e-16 ***
## vowelae:TBY       1.419e-03  2.557e-02   0.056 0.955736    
## voweli:TBY        1.313e-01  2.468e-02   5.321 1.11e-07 ***
## vowelu:TBY       -1.924e-02  1.481e-02  -1.299 0.194029    
## vowela:hyoidX     4.893e-01  3.466e-02  14.118  < 2e-16 ***
## vowelae:hyoidX   -4.144e-02  3.315e-02  -1.250 0.211331    
## voweli:hyoidX    -2.874e-01  3.085e-02  -9.316  < 2e-16 ***
## vowelu:hyoidX    -1.184e-01  2.544e-02  -4.655 3.39e-06 ***
## vowela:hyoidY    -3.536e-01  5.475e-02  -6.458 1.23e-10 ***
## vowelae:hyoidY    2.783e-01  5.461e-02   5.096 3.69e-07 ***
## voweli:hyoidY     8.149e-02  5.013e-02   1.626 0.104153    
## vowelu:hyoidY     5.671e-01  4.449e-02  12.746  < 2e-16 ***
## LEN:JA            4.126e-03  2.232e-03   1.849 0.064571 .  
## LEN:LP           -5.107e-02  7.705e-03  -6.628 4.03e-11 ***
## LEN:LD            2.675e-02  3.795e-03   7.047 2.27e-12 ***
## LEN:TCX          -1.012e-01  8.042e-03 -12.579  < 2e-16 ***
## LEN:TCY          -1.554e-01  1.232e-02 -12.615  < 2e-16 ***
## LEN:TTX          -2.555e-02  4.752e-03  -5.378 8.13e-08 ***
## LEN:TTY          -3.607e-02  4.714e-03  -7.652 2.66e-14 ***
## LEN:TBX           3.617e-03  3.348e-03   1.080 0.280058    
## LEN:TBY           3.736e-03  5.439e-03   0.687 0.492190    
## LEN:hyoidX       -1.682e-02  1.020e-02  -1.650 0.099141 .  
## LEN:hyoidY        4.811e-02  1.704e-02   2.824 0.004769 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.157 on 2917 degrees of freedom
## Multiple R-squared:  0.9281, Adjusted R-squared:  0.9261 
## F-statistic: 459.5 on 82 and 2917 DF,  p-value: < 2.2e-16
Summary of F1-F5 error regressions with betas (for non-factor DVs and ‘.’ for factors), p-values, and adjusted R2. Interactions are denoted by ‘:’.
DVs, interactions & R2 F1-F5.err
LEN 6.2 (1.2e-184***)
LEN^2 0.4 (6.9e-133***)
vowel . (0***)
JA 0.028 (0.11)
LP -0.4 (6e-11***)
LD 0.2 (3.5e-11***)
TCX -0.38 (2.9e-08***)
TCY -1.2 (2.1e-32***)
TTX -0.22 (6.9e-08***)
TTY -0.35 (7.4e-18***)
TBX -0.01 (0.72)
TBY 0.016 (0.74)
hyoidX -0.11 (0.18)
hyoidY 0.027 (0.86)
replication -0.00016 (0.12)
generation -0.00042 (6.2e-33***)
LEN:vowel . (5.7e-298***)
LEN^2:vowel . (1.4e-225***)
vowel:JA . (1.8e-44***)
vowel:LP . (3.2e-24***)
vowel:LD . (2.9e-19***)
vowel:TCX . (8.8e-35***)
vowel:TCY . (2.4e-24***)
vowel:TTX . (0.071)
vowel:TTY . (1.4e-86***)
vowel:TBX . (4.5e-12***)
vowel:TBY . (6.7e-28***)
vowel:hyoidX . (1e-56***)
vowel:hyoidY . (5.9e-84***)
LEN:JA 0.0041 (0.065)
LEN:LP -0.051 (4e-11***)
LEN:LD 0.027 (2.3e-12***)
LEN:TCX -0.1 (2.2e-35***)
LEN:TCY -0.16 (1.5e-35***)
LEN:TTX -0.026 (8.1e-08***)
LEN:TTY -0.036 (2.7e-14***)
LEN:TBX 0.0036 (0.28)
LEN:TBY 0.0037 (0.49)
LEN:hyoidX -0.017 (0.099)
LEN:hyoidY 0.048 (0.0048**)
adjusted R2 92.6%

Is larynx base height compensated by other articulators?

##                  Df Sum Sq Mean Sq F value   Pr(>F)    
## LEN               1    141   140.5  67.021 3.94e-16 ***
## I(LEN^2)          1    162   161.7  77.110  < 2e-16 ***
## vowel             4   2210   552.4 263.505  < 2e-16 ***
## replication       1      0     0.1   0.069    0.793    
## generation        1    436   435.8 207.865  < 2e-16 ***
## LEN:vowel         4    288    72.0  34.339  < 2e-16 ***
## I(LEN^2):vowel    4    118    29.5  14.093 2.14e-11 ***
## Residuals      2983   6254     2.1                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = ja.m0)
## 
## $vowel
##                diff        lwr        upr     p adj
## a-schwa  -1.4090280 -1.6371952 -1.1808608 0.0000000
## ae-schwa -2.1483893 -2.3765565 -1.9202222 0.0000000
## i-schwa  -0.6054225 -0.8335897 -0.3772553 0.0000000
## u-schwa   0.1036353 -0.1245318  0.3318025 0.7280232
## ae-a     -0.7393613 -0.9675285 -0.5111942 0.0000000
## i-a       0.8036055  0.5754383  1.0317727 0.0000000
## u-a       1.5126633  1.2844962  1.7408305 0.0000000
## i-ae      1.5429668  1.3147997  1.7711340 0.0000000
## u-ae      2.2520247  2.0238575  2.4801918 0.0000000
## u-i       0.7090578  0.4808907  0.9372250 0.0000000
## 
## Call:
## lm(formula = JA ~ LEN + I(LEN^2) + vowel + (LEN:vowel) + (I(LEN^2):vowel) + 
##     replication + generation, data = d)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.8819 -0.8777 -0.0716  0.7301  4.5636 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      -3.547e+01  4.196e+00  -8.454  < 2e-16 ***
## LEN              -8.881e+00  1.067e+00  -8.326  < 2e-16 ***
## I(LEN^2)         -5.996e-01  6.701e-02  -8.948  < 2e-16 ***
## vowela            1.905e+01  5.826e+00   3.270 0.001087 ** 
## vowelae           2.541e+01  5.823e+00   4.365 1.32e-05 ***
## voweli            3.603e+01  5.854e+00   6.155 8.53e-10 ***
## vowelu            2.833e+01  5.879e+00   4.819 1.52e-06 ***
## replication       5.228e-07  9.160e-04   0.001 0.999545    
## generation       -3.177e-03  2.806e-04 -11.322  < 2e-16 ***
## LEN:vowela        5.647e+00  1.484e+00   3.806 0.000144 ***
## LEN:vowelae       7.447e+00  1.482e+00   5.024 5.37e-07 ***
## LEN:voweli        9.670e+00  1.490e+00   6.489 1.01e-10 ***
## LEN:vowelu        8.153e+00  1.499e+00   5.439 5.81e-08 ***
## I(LEN^2):vowela   3.823e-01  9.321e-02   4.101 4.22e-05 ***
## I(LEN^2):vowelae  4.912e-01  9.310e-02   5.275 1.42e-07 ***
## I(LEN^2):voweli   6.259e-01  9.357e-02   6.689 2.67e-11 ***
## I(LEN^2):vowelu   5.724e-01  9.424e-02   6.074 1.41e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.448 on 2983 degrees of freedom
## Multiple R-squared:  0.3491, Adjusted R-squared:  0.3456 
## F-statistic: 99.99 on 16 and 2983 DF,  p-value: < 2.2e-16
##                  Df Sum Sq Mean Sq F value   Pr(>F)    
## LEN               1  101.8  101.83 553.781  < 2e-16 ***
## I(LEN^2)          1    0.2    0.23   1.268  0.26028    
## vowel             4  341.8   85.45 464.667  < 2e-16 ***
## replication       1    0.1    0.11   0.596  0.44017    
## generation        1    6.6    6.57  35.722 2.55e-09 ***
## LEN:vowel         4   48.5   12.12  65.890  < 2e-16 ***
## I(LEN^2):vowel    4    4.3    1.07   5.798  0.00012 ***
## Residuals      2983  548.5    0.18                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = lp.m0)
## 
## $vowel
##                diff         lwr        upr     p adj
## a-schwa  -0.1460782 -0.21365333 -0.0785030 0.0000000
## ae-schwa -0.4234580 -0.49103317 -0.3558828 0.0000000
## i-schwa   0.0568940 -0.01068117  0.1244692 0.1457086
## u-schwa   0.6062132  0.53863800  0.6737883 0.0000000
## ae-a     -0.2773798 -0.34495500 -0.2098047 0.0000000
## i-a       0.2029722  0.13539700  0.2705473 0.0000000
## u-a       0.7522913  0.68471617  0.8198665 0.0000000
## i-ae      0.4803520  0.41277683  0.5479272 0.0000000
## u-ae      1.0296712  0.96209600  1.0972463 0.0000000
## u-i       0.5493192  0.48174400  0.6168943 0.0000000
## 
## Call:
## lm(formula = LP ~ LEN + I(LEN^2) + vowel + (LEN:vowel) + (I(LEN^2):vowel) + 
##     replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.80042 -0.23114  0.07135  0.28776  1.39929 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      -2.886e+00  1.243e+00  -2.322 0.020283 *  
## LEN              -1.022e+00  3.159e-01  -3.234 0.001235 ** 
## I(LEN^2)         -8.321e-02  1.985e-02  -4.193 2.84e-05 ***
## vowela            6.155e+00  1.726e+00   3.567 0.000367 ***
## vowelae          -1.605e+00  1.724e+00  -0.931 0.352148    
## voweli            5.475e+00  1.734e+00   3.158 0.001606 ** 
## vowelu            2.247e+00  1.741e+00   1.291 0.196927    
## replication      -1.526e-04  2.713e-04  -0.563 0.573813    
## generation        7.524e-04  8.311e-05   9.053  < 2e-16 ***
## LEN:vowela        1.715e+00  4.395e-01   3.902 9.75e-05 ***
## LEN:vowelae      -4.394e-03  4.390e-01  -0.010 0.992015    
## LEN:voweli        1.386e+00  4.413e-01   3.140 0.001707 ** 
## LEN:vowelu        7.074e-01  4.440e-01   1.593 0.111191    
## I(LEN^2):vowela   1.136e-01  2.761e-02   4.116 3.96e-05 ***
## I(LEN^2):vowelae  1.815e-02  2.757e-02   0.658 0.510455    
## I(LEN^2):voweli   8.721e-02  2.771e-02   3.147 0.001665 ** 
## I(LEN^2):vowelu   6.128e-02  2.791e-02   2.195 0.028206 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4288 on 2983 degrees of freedom
## Multiple R-squared:  0.4785, Adjusted R-squared:  0.4757 
## F-statistic:   171 on 16 and 2983 DF,  p-value: < 2.2e-16
##                  Df Sum Sq Mean Sq F value  Pr(>F)    
## LEN               1  264.1   264.1 363.853 < 2e-16 ***
## I(LEN^2)          1    0.5     0.5   0.691 0.40591    
## vowel             4 1694.6   423.7 583.655 < 2e-16 ***
## replication       1    0.6     0.6   0.876 0.34926    
## generation        1    2.4     2.4   3.363 0.06679 .  
## LEN:vowel         4  151.1    37.8  52.047 < 2e-16 ***
## I(LEN^2):vowel    4   10.1     2.5   3.481 0.00763 ** 
## Residuals      2983 2165.3     0.7                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = ld.m0)
## 
## $vowel
##                diff         lwr         upr     p adj
## a-schwa   0.4251570  0.29089823  0.55941577 0.0000000
## ae-schwa  0.6533603  0.51910157  0.78761910 0.0000000
## i-schwa  -0.2005110 -0.33476977 -0.06625223 0.0004508
## u-schwa  -1.5014215 -1.63568027 -1.36716273 0.0000000
## ae-a      0.2282033  0.09394457  0.36246210 0.0000359
## i-a      -0.6256680 -0.75992677 -0.49140923 0.0000000
## u-a      -1.9265785 -2.06083727 -1.79231973 0.0000000
## i-ae     -0.8538713 -0.98813010 -0.71961257 0.0000000
## u-ae     -2.1547818 -2.28904060 -2.02052307 0.0000000
## u-i      -1.3009105 -1.43516927 -1.16665173 0.0000000
## 
## Call:
## lm(formula = LD ~ LEN + I(LEN^2) + vowel + (LEN:vowel) + (I(LEN^2):vowel) + 
##     replication + generation, data = d)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.0836 -0.4728 -0.1725  0.4677  3.3785 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)  
## (Intercept)      -0.2555466  2.4689425  -0.104   0.9176  
## LEN               0.0053775  0.6276095   0.009   0.9932  
## I(LEN^2)          0.0342366  0.0394307   0.868   0.3853  
## vowela           -4.7584456  3.4283985  -1.388   0.1653  
## vowelae           7.0926713  3.4261779   2.070   0.0385 *
## voweli           -7.9206179  3.4447673  -2.299   0.0216 *
## vowelu            1.3030578  3.4593881   0.377   0.7064  
## replication      -0.0005196  0.0005390  -0.964   0.3352  
## generation       -0.0002000  0.0001651  -1.211   0.2258  
## LEN:vowela       -1.6019110  0.8731453  -1.835   0.0667 .
## LEN:vowelae       1.0995689  0.8723007   1.261   0.2076  
## LEN:voweli       -1.9732284  0.8768731  -2.250   0.0245 *
## LEN:vowelu        0.2344065  0.8821025   0.266   0.7905  
## I(LEN^2):vowela  -0.1174050  0.0548488  -2.141   0.0324 *
## I(LEN^2):vowelae  0.0357496  0.0547833   0.653   0.5141  
## I(LEN^2):voweli  -0.1240167  0.0550578  -2.252   0.0244 *
## I(LEN^2):vowelu  -0.0144565  0.0554559  -0.261   0.7944  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.852 on 2983 degrees of freedom
## Multiple R-squared:  0.4951, Adjusted R-squared:  0.4924 
## F-statistic: 182.8 on 16 and 2983 DF,  p-value: < 2.2e-16
##                  Df Sum Sq Mean Sq  F value   Pr(>F)    
## LEN               1     12    12.5   59.166 1.95e-14 ***
## I(LEN^2)          1    119   118.9  562.747  < 2e-16 ***
## vowel             4   3855   963.7 4562.890  < 2e-16 ***
## replication       1      0     0.2    0.935    0.334    
## generation        1      9     8.6   40.773 1.98e-10 ***
## LEN:vowel         4    518   129.5  613.133  < 2e-16 ***
## I(LEN^2):vowel    4    269    67.2  317.965  < 2e-16 ***
## Residuals      2983    630     0.2                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = tcx.m0)
## 
## $vowel
##                diff        lwr        upr     p adj
## a-schwa  -0.2845775 -0.3569981 -0.2121569 0.0000000
## ae-schwa  1.3428832  1.2704626  1.4153038 0.0000000
## i-schwa   2.6760022  2.6035816  2.7484228 0.0000000
## u-schwa  -0.1065850 -0.1790056 -0.0341644 0.0005777
## ae-a      1.6274607  1.5550401  1.6998813 0.0000000
## i-a       2.9605797  2.8881591  3.0330003 0.0000000
## u-a       0.1779925  0.1055719  0.2504131 0.0000000
## i-ae      1.3331190  1.2606984  1.4055396 0.0000000
## u-ae     -1.4494682 -1.5218888 -1.3770476 0.0000000
## u-i      -2.7825872 -2.8550078 -2.7101666 0.0000000
## 
## Call:
## lm(formula = TCX ~ LEN + I(LEN^2) + vowel + (LEN:vowel) + (I(LEN^2):vowel) + 
##     replication + generation, data = d)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.3943 -0.1639 -0.0300  0.1428  3.5241 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      -6.755e+00  1.332e+00  -5.072 4.18e-07 ***
## LEN              -1.696e+00  3.385e-01  -5.011 5.73e-07 ***
## I(LEN^2)         -1.107e-01  2.127e-02  -5.207 2.05e-07 ***
## vowela            3.269e+00  1.849e+00   1.768 0.077188 .  
## vowelae          -6.471e+00  1.848e+00  -3.502 0.000469 ***
## voweli           -4.029e+01  1.858e+00 -21.684  < 2e-16 ***
## vowelu            1.325e+01  1.866e+00   7.098 1.57e-12 ***
## replication       2.747e-04  2.907e-04   0.945 0.344766    
## generation       -8.412e-05  8.907e-05  -0.945 0.344979    
## LEN:vowela        9.382e-01  4.710e-01   1.992 0.046459 *  
## LEN:vowelae      -1.260e+00  4.705e-01  -2.678 0.007446 ** 
## LEN:voweli       -1.153e+01  4.730e-01 -24.383  < 2e-16 ***
## LEN:vowelu        3.189e+00  4.758e-01   6.703 2.43e-11 ***
## I(LEN^2):vowela   6.083e-02  2.959e-02   2.056 0.039876 *  
## I(LEN^2):vowelae -3.433e-02  2.955e-02  -1.162 0.245438    
## I(LEN^2):voweli  -7.582e-01  2.970e-02 -25.531  < 2e-16 ***
## I(LEN^2):vowelu   1.869e-01  2.991e-02   6.248 4.75e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4596 on 2983 degrees of freedom
## Multiple R-squared:  0.8836, Adjusted R-squared:  0.883 
## F-statistic:  1415 on 16 and 2983 DF,  p-value: < 2.2e-16
##                  Df Sum Sq Mean Sq  F value   Pr(>F)    
## LEN               1  260.6  260.61 2331.909  < 2e-16 ***
## I(LEN^2)          1    2.3    2.32   20.727 5.51e-06 ***
## vowel             4  747.8  186.95 1672.815  < 2e-16 ***
## replication       1    0.0    0.05    0.446    0.504    
## generation        1    2.0    1.98   17.692 2.67e-05 ***
## LEN:vowel         4  140.2   35.04  313.539  < 2e-16 ***
## I(LEN^2):vowel    4   45.3   11.33  101.364  < 2e-16 ***
## Residuals      2983  333.4    0.11                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = tcy.m0)
## 
## $vowel
##                 diff         lwr        upr p adj
## a-schwa  -0.35678500 -0.40946602 -0.3041040 0e+00
## ae-schwa -0.25775167 -0.31043269 -0.2050706 0e+00
## i-schwa   0.99121033  0.93852931  1.0438914 0e+00
## u-schwa   0.45746000  0.40477898  0.5101410 0e+00
## ae-a      0.09903333  0.04635231  0.1517144 3e-06
## i-a       1.34799533  1.29531431  1.4006764 0e+00
## u-a       0.81424500  0.76156398  0.8669260 0e+00
## i-ae      1.24896200  1.19628098  1.3016430 0e+00
## u-ae      0.71521167  0.66253064  0.7678927 0e+00
## u-i      -0.53375033 -0.58643136 -0.4810693 0e+00
## 
## Call:
## lm(formula = TCY ~ LEN + I(LEN^2) + vowel + (LEN:vowel) + (I(LEN^2):vowel) + 
##     replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.61141 -0.11871  0.02248  0.18769  0.78563 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      -1.019e+01  9.688e-01 -10.518  < 2e-16 ***
## LEN              -2.554e+00  2.463e-01 -10.370  < 2e-16 ***
## I(LEN^2)         -1.879e-01  1.547e-02 -12.143  < 2e-16 ***
## vowela            1.690e+01  1.345e+00  12.560  < 2e-16 ***
## vowelae           2.057e+01  1.344e+00  15.304  < 2e-16 ***
## voweli           -2.374e+00  1.352e+00  -1.757   0.0791 .  
## vowelu            8.742e+00  1.357e+00   6.440 1.39e-10 ***
## replication       1.408e-04  2.115e-04   0.666   0.5055    
## generation       -4.948e-06  6.479e-05  -0.076   0.9391    
## LEN:vowela        4.314e+00  3.426e-01  12.592  < 2e-16 ***
## LEN:vowelae       5.431e+00  3.423e-01  15.868  < 2e-16 ***
## LEN:voweli       -3.239e-01  3.441e-01  -0.941   0.3466    
## LEN:vowelu        2.334e+00  3.461e-01   6.744 1.85e-11 ***
## I(LEN^2):vowela   2.653e-01  2.152e-02  12.325  < 2e-16 ***
## I(LEN^2):vowelae  3.478e-01  2.150e-02  16.179  < 2e-16 ***
## I(LEN^2):voweli   1.230e-02  2.160e-02   0.570   0.5690    
## I(LEN^2):vowelu   1.599e-01  2.176e-02   7.347 2.60e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3343 on 2983 degrees of freedom
## Multiple R-squared:  0.7823, Adjusted R-squared:  0.7812 
## F-statistic: 670.1 on 16 and 2983 DF,  p-value: < 2.2e-16
##                  Df Sum Sq Mean Sq F value   Pr(>F)    
## LEN               1   75.6   75.63 115.200  < 2e-16 ***
## I(LEN^2)          1   23.9   23.86  36.341 1.86e-09 ***
## vowel             4  203.4   50.85  77.449  < 2e-16 ***
## replication       1    0.1    0.11   0.161  0.68792    
## generation        1    7.0    6.96  10.600  0.00114 ** 
## LEN:vowel         4   59.1   14.79  22.522  < 2e-16 ***
## I(LEN^2):vowel    4   67.7   16.93  25.787  < 2e-16 ***
## Residuals      2983 1958.3    0.66                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = ttx.m0)
## 
## $vowel
##                 diff        lwr         upr     p adj
## a-schwa  -0.23025783 -0.3579402 -0.10257544 0.0000089
## ae-schwa -0.32371150 -0.4513939 -0.19602910 0.0000000
## i-schwa  -0.05966783 -0.1873502  0.06801456 0.7063628
## u-schwa  -0.73622350 -0.8639059 -0.60854110 0.0000000
## ae-a     -0.09345367 -0.2211361  0.03422873 0.2672516
## i-a       0.17059000  0.0429076  0.29827240 0.0025052
## u-a      -0.50596567 -0.6336481 -0.37828327 0.0000000
## i-ae      0.26404367  0.1363613  0.39172606 0.0000002
## u-ae     -0.41251200 -0.5401944 -0.28482960 0.0000000
## u-i      -0.67655567 -0.8042381 -0.54887327 0.0000000
## 
## Call:
## lm(formula = TTX ~ LEN + I(LEN^2) + vowel + (LEN:vowel) + (I(LEN^2):vowel) + 
##     replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.35893 -0.56159  0.01509  0.47891  2.85085 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       1.372e+01  2.348e+00   5.842 5.71e-09 ***
## LEN               2.904e+00  5.969e-01   4.865 1.20e-06 ***
## I(LEN^2)          2.006e-01  3.750e-02   5.349 9.52e-08 ***
## vowela            7.659e+00  3.260e+00   2.349  0.01889 *  
## vowelae          -8.494e+00  3.258e+00  -2.607  0.00918 ** 
## voweli           -2.042e+01  3.276e+00  -6.232 5.26e-10 ***
## vowelu           -2.949e+00  3.290e+00  -0.896  0.37015    
## replication      -2.396e-04  5.126e-04  -0.467  0.64025    
## generation       -4.468e-04  1.570e-04  -2.846  0.00446 ** 
## LEN:vowela        2.004e+00  8.304e-01   2.413  0.01587 *  
## LEN:vowelae      -2.212e+00  8.296e-01  -2.667  0.00771 ** 
## LEN:voweli       -5.595e+00  8.339e-01  -6.710 2.32e-11 ***
## LEN:vowelu       -7.506e-01  8.389e-01  -0.895  0.37096    
## I(LEN^2):vowela   1.254e-01  5.216e-02   2.405  0.01623 *  
## I(LEN^2):vowelae -1.467e-01  5.210e-02  -2.816  0.00489 ** 
## I(LEN^2):voweli  -3.756e-01  5.236e-02  -7.173 9.23e-13 ***
## I(LEN^2):vowelu  -5.802e-02  5.274e-02  -1.100  0.27136    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8102 on 2983 degrees of freedom
## Multiple R-squared:  0.1824, Adjusted R-squared:  0.178 
## F-statistic: 41.58 on 16 and 2983 DF,  p-value: < 2.2e-16
##                  Df Sum Sq Mean Sq F value   Pr(>F)    
## LEN               1  518.9   518.9 843.301  < 2e-16 ***
## I(LEN^2)          1  286.9   286.9 466.290  < 2e-16 ***
## vowel             4  193.1    48.3  78.445  < 2e-16 ***
## replication       1    0.1     0.1   0.186    0.666    
## generation        1   33.0    33.0  53.622 3.11e-13 ***
## LEN:vowel         4  209.6    52.4  85.158  < 2e-16 ***
## I(LEN^2):vowel    4   34.0     8.5  13.825 3.56e-11 ***
## Residuals      2983 1835.5     0.6                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = tty.m0)
## 
## $vowel
##                 diff        lwr         upr     p adj
## a-schwa  -0.31702217 -0.4406365 -0.19340781 0.0000000
## ae-schwa -0.34614033 -0.4697547 -0.22252598 0.0000000
## i-schwa   0.01468583 -0.1089285  0.13830019 0.9976131
## u-schwa   0.34581633  0.2222020  0.46943069 0.0000000
## ae-a     -0.02911817 -0.1527325  0.09449619 0.9679710
## i-a       0.33170800  0.2080936  0.45532236 0.0000000
## u-a       0.66283850  0.5392241  0.78645286 0.0000000
## i-ae      0.36082617  0.2372118  0.48444052 0.0000000
## u-ae      0.69195667  0.5683423  0.81557102 0.0000000
## u-i       0.33113050  0.2075161  0.45474486 0.0000000
## 
## Call:
## lm(formula = TTY ~ LEN + I(LEN^2) + vowel + (LEN:vowel) + (I(LEN^2):vowel) + 
##     replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -3.02251 -0.50607  0.07447  0.61635  1.98667 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       2.777e+01  2.273e+00  12.218  < 2e-16 ***
## LEN               6.911e+00  5.779e-01  11.961  < 2e-16 ***
## I(LEN^2)          4.054e-01  3.630e-02  11.165  < 2e-16 ***
## vowela           -2.643e+00  3.157e+00  -0.837  0.40246    
## vowelae           2.741e-02  3.155e+00   0.009  0.99307    
## voweli           -3.875e+00  3.172e+00  -1.222  0.22195    
## vowelu           -1.882e+01  3.185e+00  -5.909 3.82e-09 ***
## replication      -1.783e-04  4.963e-04  -0.359  0.71938    
## generation        4.761e-04  1.520e-04   3.131  0.00176 ** 
## LEN:vowela       -6.478e-01  8.039e-01  -0.806  0.42044    
## LEN:vowelae      -1.000e-01  8.031e-01  -0.125  0.90090    
## LEN:voweli       -4.003e-01  8.074e-01  -0.496  0.62008    
## LEN:vowelu       -4.901e+00  8.122e-01  -6.034 1.79e-09 ***
## I(LEN^2):vowela  -4.424e-02  5.050e-02  -0.876  0.38104    
## I(LEN^2):vowelae -1.800e-02  5.044e-02  -0.357  0.72130    
## I(LEN^2):voweli   1.105e-02  5.069e-02   0.218  0.82742    
## I(LEN^2):vowelu  -3.085e-01  5.106e-02  -6.042 1.71e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7844 on 2983 degrees of freedom
## Multiple R-squared:   0.41,  Adjusted R-squared:  0.4069 
## F-statistic: 129.6 on 16 and 2983 DF,  p-value: < 2.2e-16
##                  Df Sum Sq Mean Sq F value   Pr(>F)    
## LEN               1      0    0.01   0.004 0.946712    
## I(LEN^2)          1      4    4.30   3.485 0.062017 .  
## vowel             4    950  237.38 192.479  < 2e-16 ***
## replication       1      0    0.30   0.245 0.620806    
## generation        1     15   15.06  12.209 0.000483 ***
## LEN:vowel         4    231   57.68  46.770  < 2e-16 ***
## I(LEN^2):vowel    4     65   16.20  13.140  1.3e-10 ***
## Residuals      2983   3679    1.23                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = tbx.m0)
## 
## $vowel
##                diff        lwr         upr     p adj
## a-schwa  -0.2464482 -0.4214511 -0.07144519 0.0011683
## ae-schwa  0.4442950  0.2692920  0.61929797 0.0000000
## i-schwa   1.0253883  0.8503854  1.20039131 0.0000000
## u-schwa  -0.5935383 -0.7685413 -0.41853536 0.0000000
## ae-a      0.6907432  0.5157402  0.86574614 0.0000000
## i-a       1.2718365  1.0968335  1.44683947 0.0000000
## u-a      -0.3470902 -0.5220931 -0.17208719 0.0000007
## i-ae      0.5810933  0.4060904  0.75609631 0.0000000
## u-ae     -1.0378333 -1.2128363 -0.86283036 0.0000000
## u-i      -1.6189267 -1.7939296 -1.44392369 0.0000000
## 
## Call:
## lm(formula = TBX ~ LEN + I(LEN^2) + vowel + (LEN:vowel) + (I(LEN^2):vowel) + 
##     replication + generation, data = d)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.6682 -0.7449 -0.0553  0.7772  3.2908 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       7.382e+00  3.218e+00   2.294  0.02188 *  
## LEN               1.883e+00  8.181e-01   2.301  0.02143 *  
## I(LEN^2)          1.358e-01  5.140e-02   2.642  0.00829 ** 
## vowela            7.449e+00  4.469e+00   1.667  0.09565 .  
## vowelae          -8.458e+00  4.466e+00  -1.894  0.05833 .  
## voweli           -2.043e+01  4.490e+00  -4.550 5.57e-06 ***
## vowelu           -1.523e+00  4.509e+00  -0.338  0.73552    
## replication      -2.944e-04  7.026e-04  -0.419  0.67526    
## generation        7.043e-04  2.152e-04   3.272  0.00108 ** 
## LEN:vowela        1.421e+00  1.138e+00   1.248  0.21196    
## LEN:vowelae      -2.171e+00  1.137e+00  -1.909  0.05631 .  
## LEN:voweli       -6.042e+00  1.143e+00  -5.286 1.34e-07 ***
## LEN:vowelu       -6.091e-01  1.150e+00  -0.530  0.59632    
## I(LEN^2):vowela   5.560e-02  7.149e-02   0.778  0.43679    
## I(LEN^2):vowelae -1.298e-01  7.141e-02  -1.817  0.06926 .  
## I(LEN^2):voweli  -4.135e-01  7.177e-02  -5.762 9.14e-09 ***
## I(LEN^2):vowelu  -6.156e-02  7.229e-02  -0.852  0.39451    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.111 on 2983 degrees of freedom
## Multiple R-squared:  0.2558, Adjusted R-squared:  0.2518 
## F-statistic: 64.09 on 16 and 2983 DF,  p-value: < 2.2e-16
##                  Df Sum Sq Mean Sq F value  Pr(>F)    
## LEN               1   62.7    62.7 119.017 < 2e-16 ***
## I(LEN^2)          1    2.4     2.4   4.476 0.03446 *  
## vowel             4 1773.7   443.4 841.552 < 2e-16 ***
## replication       1    0.0     0.0   0.000 0.99322    
## generation        1    5.1     5.1   9.738 0.00182 ** 
## LEN:vowel         4   73.2    18.3  34.727 < 2e-16 ***
## I(LEN^2):vowel    4   54.3    13.6  25.754 < 2e-16 ***
## Residuals      2983 1571.8     0.5                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = tby.m0)
## 
## $vowel
##                diff        lwr        upr     p adj
## a-schwa  -1.2916703 -1.4060593 -1.1772813 0.0000000
## ae-schwa -0.4180947 -0.5324837 -0.3037057 0.0000000
## i-schwa   1.0970285  0.9826395  1.2114175 0.0000000
## u-schwa  -0.0884295 -0.2028185  0.0259595 0.2159371
## ae-a      0.8735757  0.7591867  0.9879647 0.0000000
## i-a       2.3886988  2.2743098  2.5030878 0.0000000
## u-a       1.2032408  1.0888518  1.3176298 0.0000000
## i-ae      1.5151232  1.4007342  1.6295122 0.0000000
## u-ae      0.3296652  0.2152762  0.4440542 0.0000000
## u-i      -1.1854580 -1.2998470 -1.0710690 0.0000000
## 
## Call:
## lm(formula = TBY ~ LEN + I(LEN^2) + vowel + (LEN:vowel) + (I(LEN^2):vowel) + 
##     replication + generation, data = d)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.8240 -0.4309  0.1024  0.4673  1.9365 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       1.861e+01  2.104e+00   8.845  < 2e-16 ***
## LEN               4.623e+00  5.347e-01   8.646  < 2e-16 ***
## I(LEN^2)          2.890e-01  3.360e-02   8.603  < 2e-16 ***
## vowela           -2.359e+01  2.921e+00  -8.076 9.65e-16 ***
## vowelae          -1.090e+01  2.919e+00  -3.735 0.000191 ***
## voweli           -2.663e+01  2.935e+00  -9.075  < 2e-16 ***
## vowelu           -1.511e+01  2.947e+00  -5.125 3.16e-07 ***
## replication       3.050e-06  4.592e-04   0.007 0.994701    
## generation       -1.127e-05  1.407e-04  -0.080 0.936174    
## LEN:vowela       -5.744e+00  7.439e-01  -7.721 1.56e-14 ***
## LEN:vowelae      -2.955e+00  7.432e-01  -3.976 7.18e-05 ***
## LEN:voweli       -7.021e+00  7.471e-01  -9.398  < 2e-16 ***
## LEN:vowelu       -4.188e+00  7.516e-01  -5.572 2.74e-08 ***
## I(LEN^2):vowela  -3.637e-01  4.673e-02  -7.782 9.78e-15 ***
## I(LEN^2):vowelae -2.024e-01  4.668e-02  -4.337 1.49e-05 ***
## I(LEN^2):voweli  -4.371e-01  4.691e-02  -9.319  < 2e-16 ***
## I(LEN^2):vowelu  -2.844e-01  4.725e-02  -6.019 1.97e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7259 on 2983 degrees of freedom
## Multiple R-squared:  0.5564, Adjusted R-squared:  0.554 
## F-statistic: 233.8 on 16 and 2983 DF,  p-value: < 2.2e-16
##                  Df Sum Sq Mean Sq F value   Pr(>F)    
## LEN               1    1.7    1.72  16.363 5.36e-05 ***
## I(LEN^2)          1   35.8   35.81 340.846  < 2e-16 ***
## vowel             4  363.3   90.84 864.594  < 2e-16 ***
## replication       1    0.1    0.10   0.923    0.337    
## generation        1    3.2    3.18  30.303 4.01e-08 ***
## LEN:vowel         4   76.1   19.02 181.024  < 2e-16 ***
## I(LEN^2):vowel    4    3.7    0.93   8.823 4.44e-07 ***
## Residuals      2983  313.4    0.11                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = hx.m0)
## 
## $vowel
##                diff         lwr         upr     p adj
## a-schwa  -0.4438560 -0.49493444 -0.39277756 0.0000000
## ae-schwa -0.2991643 -0.35024278 -0.24808589 0.0000000
## i-schwa   0.4376040  0.38652556  0.48868244 0.0000000
## u-schwa   0.3579435  0.30686506  0.40902194 0.0000000
## ae-a      0.1446917  0.09361322  0.19577011 0.0000000
## i-a       0.8814600  0.83038156  0.93253844 0.0000000
## u-a       0.8017995  0.75072106  0.85287794 0.0000000
## i-ae      0.7367683  0.68568989  0.78784678 0.0000000
## u-ae      0.6571078  0.60602939  0.70818628 0.0000000
## u-i      -0.0796605 -0.13073894 -0.02858206 0.0002073
## 
## Call:
## lm(formula = hyoidX ~ LEN + I(LEN^2) + vowel + (LEN:vowel) + 
##     (I(LEN^2):vowel) + replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.11530 -0.18256 -0.01713  0.18023  1.37779 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      -1.015e+01  9.393e-01 -10.807  < 2e-16 ***
## LEN              -2.600e+00  2.388e-01 -10.889  < 2e-16 ***
## I(LEN^2)         -1.744e-01  1.500e-02 -11.627  < 2e-16 ***
## vowela            6.854e+00  1.304e+00   5.255 1.59e-07 ***
## vowelae           2.453e+00  1.303e+00   1.882 0.059923 .  
## voweli            3.054e-01  1.311e+00   0.233 0.815781    
## vowelu            4.326e+00  1.316e+00   3.287 0.001024 ** 
## replication      -2.308e-04  2.051e-04  -1.126 0.260439    
## generation       -4.484e-04  6.282e-05  -7.138 1.18e-12 ***
## LEN:vowela        1.865e+00  3.322e-01   5.614 2.15e-08 ***
## LEN:vowelae       8.165e-01  3.319e-01   2.460 0.013935 *  
## LEN:voweli        4.020e-01  3.336e-01   1.205 0.228316    
## LEN:vowelu        1.209e+00  3.356e-01   3.602 0.000321 ***
## I(LEN^2):vowela   1.175e-01  2.087e-02   5.629 1.98e-08 ***
## I(LEN^2):vowelae  5.801e-02  2.084e-02   2.783 0.005417 ** 
## I(LEN^2):voweli   5.175e-02  2.095e-02   2.471 0.013547 *  
## I(LEN^2):vowelu   8.822e-02  2.110e-02   4.181 2.98e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3241 on 2983 degrees of freedom
## Multiple R-squared:  0.6069, Adjusted R-squared:  0.6048 
## F-statistic: 287.9 on 16 and 2983 DF,  p-value: < 2.2e-16
##                  Df Sum Sq Mean Sq   F value Pr(>F)    
## LEN               1  874.4   874.4 19253.748 <2e-16 ***
## I(LEN^2)          1    7.9     7.9   173.996 <2e-16 ***
## vowel             4   16.5     4.1    90.648 <2e-16 ***
## replication       1    0.0     0.0     0.064 0.7999    
## generation        1    0.2     0.2     3.549 0.0597 .  
## LEN:vowel         4    7.0     1.7    38.440 <2e-16 ***
## I(LEN^2):vowel    4    4.3     1.1    23.716 <2e-16 ***
## Residuals      2983  135.5     0.0                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = hy.m0)
## 
## $vowel
##                  diff         lwr          upr     p adj
## a-schwa   0.006562833 -0.02702017  0.040145838 0.9839110
## ae-schwa  0.112950833  0.07936783  0.146533838 0.0000000
## i-schwa  -0.043065500 -0.07664850 -0.009482495 0.0043015
## u-schwa  -0.114359000 -0.14794200 -0.080775995 0.0000000
## ae-a      0.106388000  0.07280500  0.139971005 0.0000000
## i-a      -0.049628333 -0.08321134 -0.016045328 0.0005394
## u-a      -0.120921833 -0.15450484 -0.087338828 0.0000000
## i-ae     -0.156016333 -0.18959934 -0.122433328 0.0000000
## u-ae     -0.227309833 -0.26089284 -0.193726828 0.0000000
## u-i      -0.071293500 -0.10487650 -0.037710495 0.0000001
## 
## Call:
## lm(formula = hyoidY ~ LEN + I(LEN^2) + vowel + (LEN:vowel) + 
##     (I(LEN^2):vowel) + replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.80504 -0.15985  0.01614  0.15060  0.60024 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      -6.950e+00  6.176e-01 -11.253  < 2e-16 ***
## LEN              -1.218e+00  1.570e-01  -7.756 1.19e-14 ***
## I(LEN^2)         -1.137e-01  9.863e-03 -11.529  < 2e-16 ***
## vowela            2.386e+00  8.576e-01   2.782  0.00543 ** 
## vowelae           6.880e+00  8.570e-01   8.028 1.41e-15 ***
## voweli            1.935e+00  8.617e-01   2.246  0.02478 *  
## vowelu            3.966e+00  8.653e-01   4.583 4.78e-06 ***
## replication       3.266e-05  1.348e-04   0.242  0.80861    
## generation       -2.000e-05  4.130e-05  -0.484  0.62823    
## LEN:vowela        6.582e-01  2.184e-01   3.013  0.00260 ** 
## LEN:vowelae       1.883e+00  2.182e-01   8.628  < 2e-16 ***
## LEN:voweli        5.761e-01  2.193e-01   2.627  0.00866 ** 
## LEN:vowelu        1.100e+00  2.206e-01   4.984 6.57e-07 ***
## I(LEN^2):vowela   4.441e-02  1.372e-02   3.237  0.00122 ** 
## I(LEN^2):vowelae  1.276e-01  1.370e-02   9.312  < 2e-16 ***
## I(LEN^2):voweli   4.050e-02  1.377e-02   2.940  0.00330 ** 
## I(LEN^2):vowelu   7.260e-02  1.387e-02   5.233 1.78e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2131 on 2983 degrees of freedom
## Multiple R-squared:  0.8704, Adjusted R-squared:  0.8698 
## F-statistic:  1253 on 16 and 2983 DF,  p-value: < 2.2e-16
##                  Df Sum Sq Mean Sq   F value  Pr(>F)    
## LEN               1   8916    8916 34456.837 < 2e-16 ***
## I(LEN^2)          1      0       0     1.390 0.23846    
## vowel             4   1741     435  1682.194 < 2e-16 ***
## replication       1      0       0     0.065 0.79850    
## generation        1      2       2     7.026 0.00808 ** 
## LEN:vowel         4    181      45   175.212 < 2e-16 ***
## I(LEN^2):vowel    4     28       7    26.668 < 2e-16 ***
## Residuals      2983    772       0                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = pc1art.m0)
## 
## $vowel
##                  diff         lwr        upr     p adj
## a-schwa  -0.837337090 -0.91749556 -0.7571786 0.0000000
## ae-schwa -0.604616068 -0.68477454 -0.5244576 0.0000000
## i-schwa   0.968036411  0.88787794  1.0481949 0.0000000
## u-schwa   0.973586733  0.89342826  1.0537452 0.0000000
## ae-a      0.232721022  0.15256255  0.3128795 0.0000000
## i-a       1.805373501  1.72521503  1.8855320 0.0000000
## u-a       1.810923822  1.73076535  1.8910823 0.0000000
## i-ae      1.572652479  1.49249400  1.6528110 0.0000000
## u-ae      1.578202801  1.49804433  1.6583613 0.0000000
## u-i       0.005550322 -0.07460815  0.0857088 0.9997155
## 
## Call:
## lm(formula = PC1.art ~ LEN + I(LEN^2) + vowel + (LEN:vowel) + 
##     (I(LEN^2):vowel) + replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.04555 -0.32109  0.02406  0.36281  1.55285 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       5.260e+00  1.474e+00   3.568 0.000365 ***
## LEN              -6.928e-01  3.747e-01  -1.849 0.064564 .  
## I(LEN^2)         -1.697e-01  2.354e-02  -7.208 7.17e-13 ***
## vowela            1.112e+01  2.047e+00   5.434 5.96e-08 ***
## vowelae           1.596e+01  2.046e+00   7.801 8.42e-15 ***
## voweli            2.498e+00  2.057e+00   1.215 0.224537    
## vowelu            5.573e+00  2.065e+00   2.698 0.007006 ** 
## replication       9.643e-05  3.218e-04   0.300 0.764475    
## generation        1.893e-04  9.858e-05   1.921 0.054883 .  
## LEN:vowela        3.167e+00  5.213e-01   6.075 1.40e-09 ***
## LEN:vowelae       4.681e+00  5.208e-01   8.987  < 2e-16 ***
## LEN:voweli        1.068e+00  5.235e-01   2.039 0.041523 *  
## LEN:vowelu        1.634e+00  5.267e-01   3.102 0.001942 ** 
## I(LEN^2):vowela   2.056e-01  3.275e-02   6.277 3.95e-10 ***
## I(LEN^2):vowelae  3.215e-01  3.271e-02   9.828  < 2e-16 ***
## I(LEN^2):voweli   1.083e-01  3.287e-02   3.294 0.000998 ***
## I(LEN^2):vowelu   1.304e-01  3.311e-02   3.937 8.44e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5087 on 2983 degrees of freedom
## Multiple R-squared:  0.9337, Adjusted R-squared:  0.9333 
## F-statistic:  2625 on 16 and 2983 DF,  p-value: < 2.2e-16
##                  Df Sum Sq Mean Sq  F value   Pr(>F)    
## LEN               1   1090  1089.5 3992.739  < 2e-16 ***
## I(LEN^2)          1    102   101.8  372.908  < 2e-16 ***
## vowel             4   4409  1102.3 4039.536  < 2e-16 ***
## replication       1      0     0.0    0.019    0.892    
## generation        1      5     5.2   19.059 1.31e-05 ***
## LEN:vowel         4    110    27.5  100.801  < 2e-16 ***
## I(LEN^2):vowel    4     57    14.2   52.063  < 2e-16 ***
## Residuals      2983    814     0.3                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = pc2art.m0)
## 
## $vowel
##                diff        lwr        upr p adj
## a-schwa  -1.3958125 -1.4781310 -1.3134941     0
## ae-schwa -0.6647254 -0.7470438 -0.5824070     0
## i-schwa   2.0773503  1.9950319  2.1596688     0
## u-schwa   0.9008470  0.8185286  0.9831654     0
## ae-a      0.7310872  0.6487687  0.8134056     0
## i-a       3.4731629  3.3908444  3.5554813     0
## u-a       2.2966595  2.2143411  2.3789780     0
## i-ae      2.7420757  2.6597573  2.8243941     0
## u-ae      1.5655724  1.4832539  1.6478908     0
## u-i      -1.1765033 -1.2588218 -1.0941849     0
## 
## Call:
## lm(formula = PC2.art ~ LEN + I(LEN^2) + vowel + (LEN:vowel) + 
##     (I(LEN^2):vowel) + replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.15856 -0.31945 -0.01013  0.34866  1.96673 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      -1.641e+01  1.514e+00 -10.840  < 2e-16 ***
## LEN              -3.776e+00  3.848e-01  -9.812  < 2e-16 ***
## I(LEN^2)         -2.132e-01  2.418e-02  -8.820  < 2e-16 ***
## vowela            9.255e+00  2.102e+00   4.403 1.11e-05 ***
## vowelae           1.672e+00  2.101e+00   0.796 0.426184    
## voweli           -1.811e+01  2.112e+00  -8.575  < 2e-16 ***
## vowelu            6.739e+00  2.121e+00   3.177 0.001503 ** 
## replication      -8.581e-05  3.305e-04  -0.260 0.795148    
## generation       -5.414e-04  1.012e-04  -5.348 9.55e-08 ***
## LEN:vowela        2.689e+00  5.354e-01   5.024 5.37e-07 ***
## LEN:vowelae       9.090e-01  5.348e-01   1.700 0.089324 .  
## LEN:voweli       -4.681e+00  5.376e-01  -8.706  < 2e-16 ***
## LEN:vowelu        1.740e+00  5.408e-01   3.217 0.001308 ** 
## I(LEN^2):vowela   1.673e-01  3.363e-02   4.976 6.86e-07 ***
## I(LEN^2):vowelae  7.588e-02  3.359e-02   2.259 0.023952 *  
## I(LEN^2):voweli  -2.650e-01  3.376e-02  -7.851 5.72e-15 ***
## I(LEN^2):vowelu   1.249e-01  3.400e-02   3.675 0.000242 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5224 on 2983 degrees of freedom
## Multiple R-squared:  0.8764, Adjusted R-squared:  0.8758 
## F-statistic:  1322 on 16 and 2983 DF,  p-value: < 2.2e-16
##                  Df Sum Sq Mean Sq  F value  Pr(>F)    
## LEN               1     96    95.8  211.773 < 2e-16 ***
## I(LEN^2)          1      1     0.6    1.308 0.25292    
## vowel             4   3354   838.4 1852.778 < 2e-16 ***
## replication       1      0     0.0    0.017 0.89773    
## generation        1      4     4.5    9.897 0.00167 ** 
## LEN:vowel         4    330    82.6  182.568 < 2e-16 ***
## I(LEN^2):vowel    4    220    55.0  121.619 < 2e-16 ***
## Residuals      2983   1350     0.5                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = pc3art.m0)
## 
## $vowel
##                 diff        lwr         upr     p adj
## a-schwa  -0.06088109 -0.1668890  0.04512681 0.5184641
## ae-schwa -1.38322834 -1.4892362 -1.27722044 0.0000000
## i-schwa  -1.60181888 -1.7078268 -1.49581098 0.0000000
## u-schwa   1.30799147  1.2019836  1.41399937 0.0000000
## ae-a     -1.32234725 -1.4283551 -1.21633935 0.0000000
## i-a      -1.54093779 -1.6469457 -1.43492989 0.0000000
## u-a       1.36887256  1.2628647  1.47488046 0.0000000
## i-ae     -0.21859054 -0.3245984 -0.11258264 0.0000002
## u-ae      2.69121981  2.5852119  2.79722771 0.0000000
## u-i       2.90981035  2.8038025  3.01581825 0.0000000
## 
## Call:
## lm(formula = PC3.art ~ LEN + I(LEN^2) + vowel + (LEN:vowel) + 
##     (I(LEN^2):vowel) + replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.47554 -0.40551  0.02374  0.44072  2.01046 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      -1.051e+01  1.949e+00  -5.391 7.57e-08 ***
## LEN              -2.980e+00  4.955e-01  -6.013 2.04e-09 ***
## I(LEN^2)         -1.990e-01  3.113e-02  -6.392 1.90e-10 ***
## vowela            1.625e+00  2.707e+00   0.600 0.548411    
## vowelae           8.098e+00  2.705e+00   2.993 0.002782 ** 
## voweli            4.363e+01  2.720e+00  16.040  < 2e-16 ***
## vowelu           -3.413e-01  2.731e+00  -0.125 0.900583    
## replication       3.207e-05  4.256e-04   0.075 0.939944    
## generation       -2.998e-04  1.304e-04  -2.299 0.021553 *  
## LEN:vowela        8.118e-01  6.894e-01   1.178 0.239069    
## LEN:vowelae       2.406e+00  6.888e-01   3.493 0.000484 ***
## LEN:voweli        1.230e+01  6.924e-01  17.769  < 2e-16 ***
## LEN:vowelu        3.160e-01  6.965e-01   0.454 0.650047    
## I(LEN^2):vowela   7.440e-02  4.331e-02   1.718 0.085910 .  
## I(LEN^2):vowelae  1.500e-01  4.326e-02   3.468 0.000531 ***
## I(LEN^2):voweli   8.183e-01  4.347e-02  18.823  < 2e-16 ***
## I(LEN^2):vowelu   6.505e-02  4.379e-02   1.486 0.137474    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6727 on 2983 degrees of freedom
## Multiple R-squared:  0.7479, Adjusted R-squared:  0.7466 
## F-statistic: 553.2 on 16 and 2983 DF,  p-value: < 2.2e-16
##                  Df Sum Sq Mean Sq   F value   Pr(>F)    
## LEN               1     11    11.3 6.946e+02  < 2e-16 ***
## I(LEN^2)          1      0     0.5 3.064e+01 3.37e-08 ***
## vowel             4   8907  2226.7 1.370e+05  < 2e-16 ***
## replication       1      0     0.0 6.570e-01    0.418    
## generation        1      2     1.7 1.057e+02  < 2e-16 ***
## LEN:vowel         4      9     2.3 1.412e+02  < 2e-16 ***
## I(LEN^2):vowel    4     11     2.8 1.749e+02  < 2e-16 ***
## Residuals      2983     48     0.0                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f1.m0)
## 
## $vowel
##                diff        lwr        upr p adj
## a-schwa   1.2662947  1.2462044  1.2863849     0
## ae-schwa  1.4269103  1.4068201  1.4470006     0
## i-schwa  -2.7444628 -2.7645531 -2.7243726     0
## u-schwa  -2.1558078 -2.1758981 -2.1357176     0
## ae-a      0.1606157  0.1405254  0.1807059     0
## i-a      -4.0107575 -4.0308478 -3.9906672     0
## u-a      -3.4221025 -3.4421928 -3.4020122     0
## i-ae     -4.1713732 -4.1914634 -4.1512829     0
## u-ae     -3.5827182 -3.6028084 -3.5626279     0
## u-i       0.5886550  0.5685647  0.6087453     0
## 
## Call:
## lm(formula = F1 ~ LEN + I(LEN^2) + vowel + (LEN:vowel) + (I(LEN^2):vowel) + 
##     replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.71892 -0.05245 -0.00138  0.05277  1.15894 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       4.624e+00  3.694e-01  12.517  < 2e-16 ***
## LEN              -1.291e-01  9.391e-02  -1.374    0.169    
## I(LEN^2)         -7.754e-03  5.900e-03  -1.314    0.189    
## vowela           -2.064e+00  5.130e-01  -4.023 5.89e-05 ***
## vowelae          -3.472e+00  5.127e-01  -6.773 1.52e-11 ***
## voweli            3.624e+00  5.155e-01   7.030 2.55e-12 ***
## vowelu            2.111e+00  5.177e-01   4.077 4.67e-05 ***
## replication       4.727e-05  8.066e-05   0.586    0.558    
## generation       -2.397e-04  2.471e-05  -9.703  < 2e-16 ***
## LEN:vowela       -8.812e-01  1.307e-01  -6.745 1.83e-11 ***
## LEN:vowelae      -1.380e+00  1.305e-01 -10.570  < 2e-16 ***
## LEN:voweli        1.571e+00  1.312e-01  11.975  < 2e-16 ***
## LEN:vowelu        9.468e-01  1.320e-01   7.173 9.21e-13 ***
## I(LEN^2):vowela  -5.706e-02  8.207e-03  -6.952 4.41e-12 ***
## I(LEN^2):vowelae -9.455e-02  8.198e-03 -11.534  < 2e-16 ***
## I(LEN^2):voweli   9.528e-02  8.239e-03  11.565  < 2e-16 ***
## I(LEN^2):vowelu   5.098e-02  8.298e-03   6.143 9.18e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1275 on 2983 degrees of freedom
## Multiple R-squared:  0.9946, Adjusted R-squared:  0.9946 
## F-statistic: 3.438e+04 on 16 and 2983 DF,  p-value: < 2.2e-16
##                  Df Sum Sq Mean Sq F value   Pr(>F)    
## LEN               1   0.40   0.405  27.682 1.53e-07 ***
## I(LEN^2)          1   3.34   3.343 228.593  < 2e-16 ***
## vowel             4   5.46   1.364  93.252  < 2e-16 ***
## replication       1   0.05   0.046   3.131   0.0769 .  
## generation        1   2.20   2.205 150.738  < 2e-16 ***
## LEN:vowel         4   7.98   1.996 136.483  < 2e-16 ***
## I(LEN^2):vowel    4   0.80   0.201  13.720 4.34e-11 ***
## Residuals      2983  43.63   0.015                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f1e.m0)
## 
## $vowel
##                  diff          lwr         upr     p adj
## a-schwa   0.054684170  0.035626048  0.07374229 0.0000000
## ae-schwa  0.046145752  0.027087629  0.06520387 0.0000000
## i-schwa   0.022666699  0.003608576  0.04172482 0.0103877
## u-schwa   0.126216379  0.107158257  0.14527450 0.0000000
## ae-a     -0.008538419 -0.027596541  0.01051970 0.7380593
## i-a      -0.032017471 -0.051075594 -0.01295935 0.0000463
## u-a       0.071532209  0.052474087  0.09059033 0.0000000
## i-ae     -0.023479053 -0.042537175 -0.00442093 0.0069959
## u-ae      0.080070628  0.061012505  0.09912875 0.0000000
## u-i       0.103549680  0.084491558  0.12260780 0.0000000
## 
## Call:
## lm(formula = F1.error ~ LEN + I(LEN^2) + vowel + (LEN:vowel) + 
##     (I(LEN^2):vowel) + replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.37891 -0.03064 -0.00755  0.01857  2.44618 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       1.018e+00  3.505e-01   2.906 0.003693 ** 
## LEN               2.513e-01  8.909e-02   2.821 0.004826 ** 
## I(LEN^2)          1.591e-02  5.597e-03   2.842 0.004519 ** 
## vowela            1.852e+00  4.867e-01   3.805 0.000144 ***
## vowelae           2.656e+00  4.863e-01   5.461 5.13e-08 ***
## voweli            1.126e+00  4.890e-01   2.303 0.021366 *  
## vowelu            3.925e+00  4.911e-01   7.993 1.86e-15 ***
## replication       1.139e-04  7.651e-05   1.489 0.136569    
## generation       -2.838e-04  2.344e-05 -12.109  < 2e-16 ***
## LEN:vowela        4.536e-01  1.239e-01   3.660 0.000257 ***
## LEN:vowelae       7.146e-01  1.238e-01   5.771 8.69e-09 ***
## LEN:voweli        2.696e-01  1.245e-01   2.166 0.030393 *  
## LEN:vowelu        8.546e-01  1.252e-01   6.825 1.06e-11 ***
## I(LEN^2):vowela   2.833e-02  7.786e-03   3.639 0.000278 ***
## I(LEN^2):vowelae  4.768e-02  7.777e-03   6.132 9.83e-10 ***
## I(LEN^2):voweli   1.616e-02  7.815e-03   2.067 0.038785 *  
## I(LEN^2):vowelu   4.688e-02  7.872e-03   5.955 2.90e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1209 on 2983 degrees of freedom
## Multiple R-squared:  0.3169, Adjusted R-squared:  0.3133 
## F-statistic:  86.5 on 16 and 2983 DF,  p-value: < 2.2e-16
##                  Df Sum Sq Mean Sq   F value Pr(>F)    
## LEN               1     44      44 2.163e+03 <2e-16 ***
## I(LEN^2)          1      7       7 3.355e+02 <2e-16 ***
## vowel             4  25939    6485 3.171e+05 <2e-16 ***
## replication       1      0       0 2.020e-01  0.653    
## generation        1      2       2 1.191e+02 <2e-16 ***
## LEN:vowel         4     61      15 7.416e+02 <2e-16 ***
## I(LEN^2):vowel    4     29       7 3.485e+02 <2e-16 ***
## Residuals      2983     61       0                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f2.m0)
## 
## $vowel
##               diff       lwr       upr p adj
## a-schwa  -1.076651 -1.099186 -1.054116     0
## ae-schwa  2.404134  2.381599  2.426669     0
## i-schwa   4.196537  4.174002  4.219072     0
## u-schwa  -4.353799 -4.376334 -4.331264     0
## ae-a      3.480784  3.458249  3.503319     0
## i-a       5.273188  5.250653  5.295723     0
## u-a      -3.277148 -3.299683 -3.254613     0
## i-ae      1.792404  1.769869  1.814939     0
## u-ae     -6.757933 -6.780468 -6.735397     0
## u-i      -8.550336 -8.572871 -8.527801     0
## 
## Call:
## lm(formula = F2 ~ LEN + I(LEN^2) + vowel + (LEN:vowel) + (I(LEN^2):vowel) + 
##     replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.76663 -0.05060 -0.00369  0.05095  1.85656 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       9.718e+00  4.144e-01  23.450  < 2e-16 ***
## LEN               5.292e-02  1.053e-01   0.502    0.615    
## I(LEN^2)          3.491e-03  6.618e-03   0.528    0.598    
## vowela           -5.281e-01  5.755e-01  -0.918    0.359    
## vowelae          -3.133e+00  5.751e-01  -5.447 5.52e-08 ***
## voweli           -7.769e+00  5.782e-01 -13.437  < 2e-16 ***
## vowelu            7.929e-01  5.807e-01   1.365    0.172    
## replication       3.067e-05  9.047e-05   0.339    0.735    
## generation       -1.318e-04  2.771e-05  -4.755 2.08e-06 ***
## LEN:vowela        1.474e-01  1.466e-01   1.006    0.315    
## LEN:vowelae      -1.536e+00  1.464e-01 -10.493  < 2e-16 ***
## LEN:voweli       -3.452e+00  1.472e-01 -23.452  < 2e-16 ***
## LEN:vowelu        1.184e+00  1.481e-01   7.996 1.83e-15 ***
## I(LEN^2):vowela   9.786e-03  9.206e-03   1.063    0.288    
## I(LEN^2):vowelae -1.040e-01  9.195e-03 -11.308  < 2e-16 ***
## I(LEN^2):voweli  -2.409e-01  9.241e-03 -26.064  < 2e-16 ***
## I(LEN^2):vowelu   6.650e-02  9.308e-03   7.144 1.13e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.143 on 2983 degrees of freedom
## Multiple R-squared:  0.9977, Adjusted R-squared:  0.9977 
## F-statistic: 7.971e+04 on 16 and 2983 DF,  p-value: < 2.2e-16
##                  Df Sum Sq Mean Sq F value  Pr(>F)    
## LEN               1  19.24  19.236 570.924 < 2e-16 ***
## I(LEN^2)          1  22.38  22.380 664.225 < 2e-16 ***
## vowel             4  50.08  12.520 371.589 < 2e-16 ***
## replication       1   0.00   0.003   0.101 0.75092    
## generation        1   0.34   0.335   9.946 0.00163 ** 
## LEN:vowel         4  93.96  23.490 697.189 < 2e-16 ***
## I(LEN^2):vowel    4  40.50  10.126 300.543 < 2e-16 ***
## Residuals      2983 100.51   0.034                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f2e.m0)
## 
## $vowel
##                  diff          lwr         upr     p adj
## a-schwa   0.009513431 -0.019412150  0.03843901 0.8978329
## ae-schwa  0.033145297  0.004219716  0.06207088 0.0153061
## i-schwa   0.346381443  0.317455863  0.37530702 0.0000000
## u-schwa   0.084291067  0.055365486  0.11321665 0.0000000
## ae-a      0.023631866 -0.005293715  0.05255745 0.1689003
## i-a       0.336868013  0.307942432  0.36579359 0.0000000
## u-a       0.074777636  0.045852055  0.10370322 0.0000000
## i-ae      0.313236146  0.284310566  0.34216173 0.0000000
## u-ae      0.051145770  0.022220189  0.08007135 0.0000144
## u-i      -0.262090376 -0.291015957 -0.23316480 0.0000000
## 
## Call:
## lm(formula = F2.error ~ LEN + I(LEN^2) + vowel + (LEN:vowel) + 
##     (I(LEN^2):vowel) + replication + generation, data = d)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.5844 -0.0373 -0.0055  0.0241  4.6120 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       1.008e+00  5.319e-01   1.895 0.058149 .  
## LEN               2.476e-01  1.352e-01   1.831 0.067161 .  
## I(LEN^2)          1.577e-02  8.495e-03   1.856 0.063506 .  
## vowela           -1.668e-01  7.386e-01  -0.226 0.821363    
## vowelae           2.359e+00  7.382e-01   3.196 0.001409 ** 
## voweli            1.837e+01  7.422e-01  24.759  < 2e-16 ***
## vowelu            4.199e+00  7.453e-01   5.633 1.93e-08 ***
## replication      -5.927e-05  1.161e-04  -0.510 0.609829    
## generation       -2.970e-04  3.557e-05  -8.349  < 2e-16 ***
## LEN:vowela       -5.560e-02  1.881e-01  -0.296 0.767572    
## LEN:vowelae       6.324e-01  1.879e-01   3.365 0.000775 ***
## LEN:voweli        5.037e+00  1.889e-01  26.662  < 2e-16 ***
## LEN:vowelu        9.655e-01  1.900e-01   5.080 4.00e-07 ***
## I(LEN^2):vowela  -3.950e-03  1.182e-02  -0.334 0.738172    
## I(LEN^2):vowelae  4.193e-02  1.180e-02   3.552 0.000388 ***
## I(LEN^2):voweli   3.426e-01  1.186e-02  28.882  < 2e-16 ***
## I(LEN^2):vowelu   5.571e-02  1.195e-02   4.663 3.26e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1836 on 2983 degrees of freedom
## Multiple R-squared:  0.6926, Adjusted R-squared:  0.691 
## F-statistic: 420.2 on 16 and 2983 DF,  p-value: < 2.2e-16
##                  Df Sum Sq Mean Sq  F value Pr(>F)    
## LEN               1  213.5  213.47 2299.192 <2e-16 ***
## I(LEN^2)          1   94.8   94.78 1020.771 <2e-16 ***
## vowel             4  397.4   99.36 1070.144 <2e-16 ***
## replication       1    0.0    0.00    0.044  0.834    
## generation        1    0.2    0.23    2.434  0.119    
## LEN:vowel         4   19.2    4.79   51.644 <2e-16 ***
## I(LEN^2):vowel    4   24.7    6.18   66.539 <2e-16 ***
## Residuals      2983  277.0    0.09                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f3.m0)
## 
## $vowel
##                diff         lwr        upr   p adj
## a-schwa   0.3796662  0.33164887  0.4276835 0.0e+00
## ae-schwa  0.1479860  0.09996871  0.1960033 0.0e+00
## i-schwa   1.0587442  1.01072687  1.1067615 0.0e+00
## u-schwa   0.4722282  0.42421087  0.5202455 0.0e+00
## ae-a     -0.2316802 -0.27969746 -0.1836629 0.0e+00
## i-a       0.6790780  0.63106071  0.7270953 0.0e+00
## u-a       0.0925620  0.04454471  0.1405793 1.5e-06
## i-ae      0.9107582  0.86274087  0.9587755 0.0e+00
## u-ae      0.3242422  0.27622487  0.3722595 0.0e+00
## u-i      -0.5865160 -0.63453329 -0.5384987 0.0e+00
## 
## Call:
## lm(formula = F3 ~ LEN + I(LEN^2) + vowel + (LEN:vowel) + (I(LEN^2):vowel) + 
##     replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.78577 -0.10898 -0.00001  0.10983  1.82683 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       2.141e+00  8.830e-01   2.424   0.0154 *  
## LEN              -3.373e+00  2.245e-01 -15.028  < 2e-16 ***
## I(LEN^2)         -2.273e-01  1.410e-02 -16.118  < 2e-16 ***
## vowela           -6.354e+00  1.226e+00  -5.182 2.34e-07 ***
## vowelae          -5.794e-01  1.225e+00  -0.473   0.6364    
## voweli            6.758e+00  1.232e+00   5.486 4.47e-08 ***
## vowelu            1.151e+01  1.237e+00   9.303  < 2e-16 ***
## replication       4.658e-05  1.928e-04   0.242   0.8091    
## generation        8.062e-05  5.905e-05   1.365   0.1723    
## LEN:vowela       -1.857e+00  3.123e-01  -5.946 3.07e-09 ***
## LEN:vowelae      -1.945e-01  3.120e-01  -0.623   0.5331    
## LEN:voweli        1.566e+00  3.136e-01   4.994 6.27e-07 ***
## LEN:vowelu        2.765e+00  3.155e-01   8.763  < 2e-16 ***
## I(LEN^2):vowela  -1.250e-01  1.962e-02  -6.371 2.16e-10 ***
## I(LEN^2):vowelae -1.271e-02  1.959e-02  -0.649   0.5166    
## I(LEN^2):voweli   1.051e-01  1.969e-02   5.336 1.02e-07 ***
## I(LEN^2):vowelu   1.702e-01  1.983e-02   8.581  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3047 on 2983 degrees of freedom
## Multiple R-squared:  0.7303, Adjusted R-squared:  0.7288 
## F-statistic: 504.7 on 16 and 2983 DF,  p-value: < 2.2e-16
##                  Df Sum Sq Mean Sq  F value Pr(>F)    
## LEN               1  336.8   336.8 2401.950 <2e-16 ***
## I(LEN^2)          1  205.5   205.5 1465.412 <2e-16 ***
## vowel             4   72.2    18.0  128.683 <2e-16 ***
## replication       1    0.0     0.0    0.063  0.801    
## generation        1   18.3    18.3  130.308 <2e-16 ***
## LEN:vowel         4   91.4    22.8  162.889 <2e-16 ***
## I(LEN^2):vowel    4   61.0    15.3  108.804 <2e-16 ***
## Residuals      2983  418.3     0.1                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f3e.m0)
## 
## $vowel
##                 diff         lwr         upr     p adj
## a-schwa   0.24590068  0.18689104  0.30491032 0.0000000
## ae-schwa  0.01228932 -0.04672032  0.07129896 0.9796108
## i-schwa  -0.02238000 -0.08138964  0.03662964 0.8390675
## u-schwa   0.36119025  0.30218060  0.42019989 0.0000000
## ae-a     -0.23361136 -0.29262100 -0.17460172 0.0000000
## i-a      -0.26828068 -0.32729032 -0.20927104 0.0000000
## u-a       0.11528957  0.05627992  0.17429921 0.0000010
## i-ae     -0.03466932 -0.09367896  0.02434032 0.4951256
## u-ae      0.34890093  0.28989128  0.40791057 0.0000000
## u-i       0.38357025  0.32456060  0.44257989 0.0000000
## 
## Call:
## lm(formula = F3.error ~ LEN + I(LEN^2) + vowel + (LEN:vowel) + 
##     (I(LEN^2):vowel) + replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.85790 -0.11849 -0.00991  0.10380  2.67903 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       1.373e+01  1.085e+00  12.651  < 2e-16 ***
## LEN               3.681e+00  2.758e-01  13.343  < 2e-16 ***
## I(LEN^2)          2.454e-01  1.733e-02  14.160  < 2e-16 ***
## vowela            1.678e+01  1.507e+00  11.133  < 2e-16 ***
## vowelae          -1.956e+00  1.506e+00  -1.299    0.194    
## voweli           -8.459e+00  1.514e+00  -5.587 2.51e-08 ***
## vowelu            8.111e+00  1.520e+00   5.335 1.03e-07 ***
## replication       2.269e-05  2.369e-04   0.096    0.924    
## generation       -4.896e-04  7.257e-05  -6.746 1.82e-11 ***
## LEN:vowela        4.536e+00  3.838e-01  11.821  < 2e-16 ***
## LEN:vowelae      -5.201e-01  3.834e-01  -1.357    0.175    
## LEN:voweli       -2.257e+00  3.854e-01  -5.857 5.22e-09 ***
## LEN:vowelu        2.299e+00  3.877e-01   5.929 3.39e-09 ***
## I(LEN^2):vowela   3.043e-01  2.411e-02  12.624  < 2e-16 ***
## I(LEN^2):vowelae -3.392e-02  2.408e-02  -1.409    0.159    
## I(LEN^2):voweli  -1.480e-01  2.420e-02  -6.118 1.07e-09 ***
## I(LEN^2):vowelu   1.643e-01  2.437e-02   6.740 1.90e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3745 on 2983 degrees of freedom
## Multiple R-squared:  0.6524, Adjusted R-squared:  0.6506 
## F-statistic:   350 on 16 and 2983 DF,  p-value: < 2.2e-16
##                  Df Sum Sq Mean Sq F value   Pr(>F)    
## LEN               1  65.88   65.88 915.085  < 2e-16 ***
## I(LEN^2)          1   0.56    0.56   7.716  0.00551 ** 
## vowel             4 164.02   41.00 569.533  < 2e-16 ***
## replication       1   0.04    0.04   0.539  0.46289    
## generation        1   2.81    2.81  39.088 4.63e-10 ***
## LEN:vowel         4  19.05    4.76  66.166  < 2e-16 ***
## I(LEN^2):vowel    4  20.82    5.21  72.300  < 2e-16 ***
## Residuals      2983 214.76    0.07                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f4.m0)
## 
## $vowel
##                 diff          lwr          upr     p adj
## a-schwa  -0.18706467 -0.229347849 -0.144781484 0.0000000
## ae-schwa  0.03495083 -0.007332349  0.077234016 0.1596788
## i-schwa   0.50373283  0.461449651  0.546016016 0.0000000
## u-schwa  -0.04582850 -0.088111682 -0.003545318 0.0258936
## ae-a      0.22201550  0.179732318  0.264298682 0.0000000
## i-a       0.69079750  0.648514318  0.733080682 0.0000000
## u-a       0.14123617  0.098952984  0.183519349 0.0000000
## i-ae      0.46878200  0.426498818  0.511065182 0.0000000
## u-ae     -0.08077933 -0.123062516 -0.038496151 0.0000020
## u-i      -0.54956133 -0.591844516 -0.507278151 0.0000000
## 
## Call:
## lm(formula = F4 ~ LEN + I(LEN^2) + vowel + (LEN:vowel) + (I(LEN^2):vowel) + 
##     replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.31160 -0.13988 -0.02858  0.09520  1.64294 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      12.2559754  0.7775637  15.762  < 2e-16 ***
## LEN              -1.0363722  0.1976581  -5.243 1.69e-07 ***
## I(LEN^2)         -0.0680677  0.0124182  -5.481 4.58e-08 ***
## vowela           -1.8431068  1.0797328  -1.707  0.08793 .  
## vowelae           2.8151681  1.0790335   2.609  0.00913 ** 
## voweli            8.0354463  1.0848880   7.407 1.68e-13 ***
## vowelu           13.8142052  1.0894926  12.679  < 2e-16 ***
## replication       0.0001035  0.0001698   0.610  0.54197    
## generation       -0.0002791  0.0000520  -5.368 8.59e-08 ***
## LEN:vowela       -0.6025396  0.2749866  -2.191  0.02852 *  
## LEN:vowelae       0.4976349  0.2747206   1.811  0.07018 .  
## LEN:voweli        1.8445077  0.2761606   6.679 2.86e-11 ***
## LEN:vowelu        3.4884375  0.2778076  12.557  < 2e-16 ***
## I(LEN^2):vowela  -0.0486044  0.0172740  -2.814  0.00493 ** 
## I(LEN^2):vowelae  0.0181883  0.0172534   1.054  0.29188    
## I(LEN^2):voweli   0.1109727  0.0173398   6.400 1.80e-10 ***
## I(LEN^2):vowelu   0.2161769  0.0174651  12.378  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2683 on 2983 degrees of freedom
## Multiple R-squared:  0.5599, Adjusted R-squared:  0.5575 
## F-statistic: 237.2 on 16 and 2983 DF,  p-value: < 2.2e-16
##                  Df Sum Sq Mean Sq F value Pr(>F)    
## LEN               1   0.11   0.114   1.300  0.254    
## I(LEN^2)          1   6.12   6.125  69.930 <2e-16 ***
## vowel             4  23.65   5.912  67.500 <2e-16 ***
## replication       1   0.00   0.004   0.043  0.835    
## generation        1  13.71  13.707 156.508 <2e-16 ***
## LEN:vowel         4  14.76   3.691  42.146 <2e-16 ***
## I(LEN^2):vowel    4  12.96   3.240  36.996 <2e-16 ***
## Residuals      2983 261.26   0.088                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f4e.m0)
## 
## $vowel
##                 diff         lwr         upr     p adj
## a-schwa   0.07531938  0.02868309 0.121955664 0.0001054
## ae-schwa  0.08824385  0.04160756 0.134880140 0.0000025
## i-schwa   0.05149025  0.00485396 0.098126536 0.0218916
## u-schwa   0.26251898  0.21588269 0.309155268 0.0000000
## ae-a      0.01292448 -0.03371181 0.059560763 0.9428703
## i-a      -0.02382913 -0.07046542 0.022807160 0.6311783
## u-a       0.18719960  0.14056332 0.233835892 0.0000000
## i-ae     -0.03675360 -0.08338989 0.009882684 0.1989404
## u-ae      0.17427513  0.12763884 0.220911417 0.0000000
## u-i       0.21102873  0.16439244 0.257665020 0.0000000
## 
## Call:
## lm(formula = F4.error ~ LEN + I(LEN^2) + vowel + (LEN:vowel) + 
##     (I(LEN^2):vowel) + replication + generation, data = d)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.7485 -0.0849 -0.0326  0.0459  4.3436 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       1.402e+00  8.576e-01   1.635 0.102142    
## LEN               3.421e-01  2.180e-01   1.569 0.116715    
## I(LEN^2)          2.249e-02  1.370e-02   1.642 0.100658    
## vowela           -1.963e+00  1.191e+00  -1.648 0.099435 .  
## vowelae           3.470e+00  1.190e+00   2.916 0.003575 ** 
## voweli            5.162e-01  1.197e+00   0.431 0.666239    
## vowelu            1.197e+01  1.202e+00   9.960  < 2e-16 ***
## replication      -5.014e-06  1.872e-04  -0.027 0.978636    
## generation       -5.833e-04  5.736e-05 -10.170  < 2e-16 ***
## LEN:vowela       -5.247e-01  3.033e-01  -1.730 0.083725 .  
## LEN:vowelae       9.642e-01  3.030e-01   3.182 0.001477 ** 
## LEN:voweli        5.172e-02  3.046e-01   0.170 0.865170    
## LEN:vowelu        2.871e+00  3.064e-01   9.371  < 2e-16 ***
## I(LEN^2):vowela  -3.284e-02  1.905e-02  -1.724 0.084868 .  
## I(LEN^2):vowelae  6.643e-02  1.903e-02   3.491 0.000489 ***
## I(LEN^2):voweli  -8.923e-04  1.912e-02  -0.047 0.962790    
## I(LEN^2):vowelu   1.736e-01  1.926e-02   9.014  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2959 on 2983 degrees of freedom
## Multiple R-squared:  0.2145, Adjusted R-squared:  0.2102 
## F-statistic:  50.9 on 16 and 2983 DF,  p-value: < 2.2e-16
##                  Df Sum Sq Mean Sq  F value Pr(>F)    
## LEN               1  65.93   65.93 1520.677 <2e-16 ***
## I(LEN^2)          1  77.15   77.15 1779.445 <2e-16 ***
## vowel             4 106.48   26.62  613.995 <2e-16 ***
## replication       1   0.03    0.03    0.744  0.389    
## generation        1   6.42    6.42  148.158 <2e-16 ***
## LEN:vowel         4  19.37    4.84  111.700 <2e-16 ***
## I(LEN^2):vowel    4  90.46   22.62  521.652 <2e-16 ***
## Residuals      2983 129.33    0.04                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f5.m0)
## 
## $vowel
##                 diff          lwr          upr     p adj
## a-schwa   0.02494017 -0.007871841  0.057752175 0.2313571
## ae-schwa  0.09895817  0.066146159  0.131770175 0.0000000
## i-schwa  -0.03595900 -0.068771008 -0.003146992 0.0234372
## u-schwa  -0.43585017 -0.468662175 -0.403038159 0.0000000
## ae-a      0.07401800  0.041205992  0.106830008 0.0000000
## i-a      -0.06089917 -0.093711175 -0.028087159 0.0000043
## u-a      -0.46079033 -0.493602341 -0.427978325 0.0000000
## i-ae     -0.13491717 -0.167729175 -0.102105159 0.0000000
## u-ae     -0.53480833 -0.567620341 -0.501996325 0.0000000
## u-i      -0.39989117 -0.432703175 -0.367079159 0.0000000
## 
## Call:
## lm(formula = F5 ~ LEN + I(LEN^2) + vowel + (LEN:vowel) + (I(LEN^2):vowel) + 
##     replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.16825 -0.10985  0.00877  0.09293  1.36548 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       2.332e+01  6.034e-01  38.655  < 2e-16 ***
## LEN               1.265e+00  1.534e-01   8.248 2.39e-16 ***
## I(LEN^2)          7.574e-02  9.637e-03   7.859 5.34e-15 ***
## vowela            2.452e+00  8.379e-01   2.927  0.00345 ** 
## vowelae           1.138e-01  8.373e-01   0.136  0.89191    
## voweli            2.532e+00  8.419e-01   3.007  0.00266 ** 
## vowelu            3.242e+01  8.455e-01  38.343  < 2e-16 ***
## replication      -1.388e-04  1.317e-04  -1.054  0.29212    
## generation       -3.344e-04  4.035e-05  -8.286  < 2e-16 ***
## LEN:vowela        5.222e-01  2.134e-01   2.447  0.01446 *  
## LEN:vowelae      -9.328e-02  2.132e-01  -0.438  0.66174    
## LEN:voweli        6.251e-01  2.143e-01   2.917  0.00356 ** 
## LEN:vowelu        8.173e+00  2.156e-01  37.911  < 2e-16 ***
## I(LEN^2):vowela   2.704e-02  1.340e-02   2.017  0.04376 *  
## I(LEN^2):vowelae -1.191e-02  1.339e-02  -0.890  0.37380    
## I(LEN^2):voweli   3.734e-02  1.346e-02   2.775  0.00555 ** 
## I(LEN^2):vowelu   5.002e-01  1.355e-02  36.910  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2082 on 2983 degrees of freedom
## Multiple R-squared:  0.7388, Adjusted R-squared:  0.7374 
## F-statistic: 527.4 on 16 and 2983 DF,  p-value: < 2.2e-16
##                  Df Sum Sq Mean Sq  F value Pr(>F)    
## LEN               1   78.9   78.94  826.584 <2e-16 ***
## I(LEN^2)          1  162.8  162.76 1704.212 <2e-16 ***
## vowel             4  363.9   90.98  952.642 <2e-16 ***
## replication       1    0.1    0.07    0.707  0.401    
## generation        1   14.3   14.30  149.726 <2e-16 ***
## LEN:vowel         4  170.6   42.65  446.635 <2e-16 ***
## I(LEN^2):vowel    4  349.2   87.30  914.151 <2e-16 ***
## Residuals      2983  284.9    0.10                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = f5e.m0)
## 
## $vowel
##                 diff          lwr        upr     p adj
## a-schwa  0.017963483 -0.030735666 0.06666263 0.8523528
## ae-schwa 0.023620836 -0.025078313 0.07231998 0.6763185
## i-schwa  0.050998397  0.002299248 0.09969755 0.0347793
## u-schwa  0.892911019  0.844211871 0.94161017 0.0000000
## ae-a     0.005657353 -0.043041796 0.05435650 0.9978132
## i-a      0.033034914 -0.015664234 0.08173406 0.3441483
## u-a      0.874947537  0.826248388 0.92364669 0.0000000
## i-ae     0.027377561 -0.021321587 0.07607671 0.5400289
## u-ae     0.869290184  0.820591035 0.91798933 0.0000000
## u-i      0.841912622  0.793213474 0.89061177 0.0000000
## 
## Call:
## lm(formula = F5.error ~ LEN + I(LEN^2) + vowel + (LEN:vowel) + 
##     (I(LEN^2):vowel) + replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.70174 -0.05366 -0.00684  0.03785  2.68674 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       4.010e+00  8.955e-01   4.477 7.84e-06 ***
## LEN               9.752e-01  2.277e-01   4.284 1.90e-05 ***
## I(LEN^2)          5.998e-02  1.430e-02   4.193 2.83e-05 ***
## vowela            1.577e+00  1.244e+00   1.268    0.205    
## vowelae           1.750e+00  1.243e+00   1.408    0.159    
## voweli            1.992e+00  1.250e+00   1.594    0.111    
## vowelu            6.642e+01  1.255e+00  52.932  < 2e-16 ***
## replication      -1.971e-04  1.955e-04  -1.008    0.313    
## generation       -4.353e-04  5.989e-05  -7.269 4.61e-13 ***
## LEN:vowela        3.451e-01  3.167e-01   1.089    0.276    
## LEN:vowelae       4.184e-01  3.164e-01   1.322    0.186    
## LEN:voweli        4.585e-01  3.181e-01   1.441    0.150    
## LEN:vowelu        1.614e+01  3.200e-01  50.436  < 2e-16 ***
## I(LEN^2):vowela   1.870e-02  1.990e-02   0.940    0.347    
## I(LEN^2):vowelae  2.471e-02  1.987e-02   1.244    0.214    
## I(LEN^2):voweli   2.648e-02  1.997e-02   1.326    0.185    
## I(LEN^2):vowelu   9.773e-01  2.012e-02  48.584  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.309 on 2983 degrees of freedom
## Multiple R-squared:    0.8,  Adjusted R-squared:  0.799 
## F-statistic: 745.9 on 16 and 2983 DF,  p-value: < 2.2e-16
##                  Df Sum Sq Mean Sq   F value Pr(>F)    
## LEN               1   7596    7596 28288.471 <2e-16 ***
## I(LEN^2)          1     53      53   196.091 <2e-16 ***
## vowel             4   5963    1491  5552.210 <2e-16 ***
## replication       1      0       0     0.201  0.654    
## generation        1      0       0     0.939  0.333    
## LEN:vowel         4    188      47   175.319 <2e-16 ***
## I(LEN^2):vowel    4     68      17    63.315 <2e-16 ***
## Residuals      2983    801       0                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = pc1.m0)
## 
## $vowel
##                diff        lwr        upr p adj
## a-schwa  -1.0929117 -1.1745688 -1.0112546     0
## ae-schwa -0.4766921 -0.5583492 -0.3950350     0
## i-schwa   2.9010057  2.8193486  2.9826628     0
## u-schwa   1.1578212  1.0761641  1.2394783     0
## ae-a      0.6162196  0.5345625  0.6978767     0
## i-a       3.9939175  3.9122604  4.0755746     0
## u-a       2.2507330  2.1690759  2.3323901     0
## i-ae      3.3776979  3.2960408  3.4593550     0
## u-ae      1.6345134  1.5528563  1.7161705     0
## u-i      -1.7431845 -1.8248416 -1.6615274     0
## 
## Call:
## lm(formula = PC1 ~ LEN + I(LEN^2) + vowel + (LEN:vowel) + (I(LEN^2):vowel) + 
##     replication + generation, data = d)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.9050 -0.2699  0.0102  0.2812  2.4989 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      -7.2745252  1.5016277  -4.844 1.33e-06 ***
## LEN              -3.5196863  0.3817164  -9.221  < 2e-16 ***
## I(LEN^2)         -0.3298058  0.0239820 -13.752  < 2e-16 ***
## vowela            6.3839273  2.0851754   3.062  0.00222 ** 
## vowelae          15.0094862  2.0838248   7.203 7.43e-13 ***
## voweli            3.5257552  2.0951310   1.683  0.09251 .  
## vowelu           28.4046665  2.1040235  13.500  < 2e-16 ***
## replication       0.0001372  0.0003278   0.418  0.67569    
## generation       -0.0001301  0.0001004  -1.296  0.19513    
## LEN:vowela        1.7304347  0.5310529   3.258  0.00113 ** 
## LEN:vowelae       4.2151226  0.5305392   7.945 2.73e-15 ***
## LEN:voweli        0.7220936  0.5333202   1.354  0.17585    
## LEN:vowelu        7.2126556  0.5365008  13.444  < 2e-16 ***
## I(LEN^2):vowela   0.0978224  0.0333594   2.932  0.00339 ** 
## I(LEN^2):vowelae  0.2804658  0.0333196   8.417  < 2e-16 ***
## I(LEN^2):voweli   0.0796083  0.0334865   2.377  0.01750 *  
## I(LEN^2):vowelu   0.4684896  0.0337286  13.890  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5182 on 2983 degrees of freedom
## Multiple R-squared:  0.9454, Adjusted R-squared:  0.9451 
## F-statistic:  3228 on 16 and 2983 DF,  p-value: < 2.2e-16
##                  Df Sum Sq Mean Sq   F value Pr(>F)    
## LEN               1   3021  3021.4 14268.920 <2e-16 ***
## I(LEN^2)          1    202   202.5   956.330 <2e-16 ***
## vowel             4   5277  1319.2  6230.173 <2e-16 ***
## replication       1      0     0.0     0.009  0.922    
## generation        1      1     0.6     2.670  0.102    
## LEN:vowel         4    137    34.3   161.943 <2e-16 ***
## I(LEN^2):vowel    4     89    22.1   104.490 <2e-16 ***
## Residuals      2983    632     0.2                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = pc2.m0)
## 
## $vowel
##                diff        lwr        upr p adj
## a-schwa   1.0899037  1.0173898  1.1624176     0
## ae-schwa  1.3862569  1.3137429  1.4587708     0
## i-schwa  -1.2178188 -1.2903328 -1.1453049     0
## u-schwa  -2.0827940 -2.1553079 -2.0102801     0
## ae-a      0.2963531  0.2238392  0.3688671     0
## i-a      -2.3077225 -2.3802365 -2.2352086     0
## u-a      -3.1726977 -3.2452116 -3.1001838     0
## i-ae     -2.6040757 -2.6765896 -2.5315618     0
## u-ae     -3.4690508 -3.5415648 -3.3965369     0
## u-i      -0.8649752 -0.9374891 -0.7924612     0
## 
## Call:
## lm(formula = PC2 ~ LEN + I(LEN^2) + vowel + (LEN:vowel) + (I(LEN^2):vowel) + 
##     replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.91833 -0.29979  0.02253  0.28418  2.18984 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       2.043e+01  1.333e+00  15.320  < 2e-16 ***
## LEN               4.487e+00  3.390e-01  13.238  < 2e-16 ***
## I(LEN^2)          2.399e-01  2.130e-02  11.263  < 2e-16 ***
## vowela           -4.748e+00  1.852e+00  -2.564 0.010384 *  
## vowelae          -4.967e-01  1.850e+00  -0.268 0.788405    
## voweli            2.873e+00  1.861e+00   1.544 0.122603    
## vowelu            2.900e+01  1.868e+00  15.521  < 2e-16 ***
## replication      -2.772e-05  2.911e-04  -0.095 0.924148    
## generation        8.494e-06  8.918e-05   0.095 0.924125    
## LEN:vowela       -1.676e+00  4.716e-01  -3.553 0.000386 ***
## LEN:vowelae      -7.881e-01  4.711e-01  -1.673 0.094469 .  
## LEN:voweli        5.631e-01  4.736e-01   1.189 0.234530    
## LEN:vowelu        7.345e+00  4.764e-01  15.417  < 2e-16 ***
## I(LEN^2):vowela  -1.165e-01  2.962e-02  -3.932 8.62e-05 ***
## I(LEN^2):vowelae -6.821e-02  2.959e-02  -2.305 0.021228 *  
## I(LEN^2):voweli   6.002e-03  2.974e-02   0.202 0.840046    
## I(LEN^2):vowelu   4.250e-01  2.995e-02  14.190  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4602 on 2983 degrees of freedom
## Multiple R-squared:  0.9325, Adjusted R-squared:  0.9321 
## F-statistic:  2576 on 16 and 2983 DF,  p-value: < 2.2e-16
##                  Df Sum Sq Mean Sq  F value   Pr(>F)    
## LEN               1    914   913.6 3389.574  < 2e-16 ***
## I(LEN^2)          1     13    13.1   48.617 3.82e-12 ***
## vowel             4   6612  1653.1 6133.002  < 2e-16 ***
## replication       1      0     0.0    0.001     0.98    
## generation        1      5     5.2   19.282 1.17e-05 ***
## LEN:vowel         4    191    47.6  176.741  < 2e-16 ***
## I(LEN^2):vowel    4    196    48.9  181.486  < 2e-16 ***
## Residuals      2983    804     0.3                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = pc3.m0)
## 
## $vowel
##                diff       lwr        upr p adj
## a-schwa  -0.4037544 -0.485567 -0.3219417     0
## ae-schwa  1.3453207  1.263508  1.4271334     0
## i-schwa   2.6019135  2.520101  2.6837261     0
## u-schwa  -1.7161854 -1.797998 -1.6343728     0
## ae-a      1.7490751  1.667262  1.8308878     0
## i-a       3.0056678  2.923855  3.0874805     0
## u-a      -1.3124311 -1.394244 -1.2306184     0
## i-ae      1.2565927  1.174780  1.3384054     0
## u-ae     -3.0615062 -3.143319 -2.9796935     0
## u-i      -4.3180989 -4.399912 -4.2362863     0
## 
## Call:
## lm(formula = PC3 ~ LEN + I(LEN^2) + vowel + (LEN:vowel) + (I(LEN^2):vowel) + 
##     replication + generation, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.64753 -0.32629 -0.03025  0.28593  2.23827 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      -3.580e+00  1.504e+00  -2.380 0.017397 *  
## LEN               1.147e-01  3.824e-01   0.300 0.764223    
## I(LEN^2)          6.539e-02  2.403e-02   2.721 0.006541 ** 
## vowela           -4.981e+00  2.089e+00  -2.384 0.017182 *  
## vowelae          -8.372e+00  2.088e+00  -4.010 6.22e-05 ***
## voweli           -2.993e+01  2.099e+00 -14.258  < 2e-16 ***
## vowelu            2.078e+01  2.108e+00   9.856  < 2e-16 ***
## replication      -4.251e-05  3.284e-04  -0.129 0.897022    
## generation       -4.546e-04  1.006e-04  -4.518 6.47e-06 ***
## LEN:vowela       -1.609e+00  5.321e-01  -3.024 0.002518 ** 
## LEN:vowelae      -2.746e+00  5.315e-01  -5.166 2.55e-07 ***
## LEN:voweli       -8.944e+00  5.343e-01 -16.738  < 2e-16 ***
## LEN:vowelu        5.041e+00  5.375e-01   9.378  < 2e-16 ***
## I(LEN^2):vowela  -1.275e-01  3.342e-02  -3.816 0.000138 ***
## I(LEN^2):vowelae -1.887e-01  3.338e-02  -5.653 1.73e-08 ***
## I(LEN^2):voweli  -6.003e-01  3.355e-02 -17.894  < 2e-16 ***
## I(LEN^2):vowelu   2.741e-01  3.379e-02   8.110 7.33e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5192 on 2983 degrees of freedom
## Multiple R-squared:  0.9079, Adjusted R-squared:  0.9075 
## F-statistic:  1839 on 16 and 2983 DF,  p-value: < 2.2e-16
Summary of regressions of articulators on VT ratio with betas (for non-factor DVs and ‘.’ for factors), p-values, and adjusted R2. Interactions are denoted by ‘:’.
DVs, interactions & R2 JA LP LD TCX TCY TTX TTY TBX TBY hyoidX hyoidY PC1(art) PC2(art) PC3(art) F1 F1.err F2 F2.err F3 F3.err F4 F4.err F5 F5.err PC1(all) PC2(all) PC3(all)
LEN -8.9 (1.3e-16***) -1 (0.0012**) 0.0054 (0.99) -1.7 (5.7e-07***) -2.6 (8.9e-25***) 2.9 (1.2e-06***) 6.9 (3.1e-32***) 1.9 (0.021*) 4.6 (8.5e-18***) -2.6 (4.2e-27***) -1.2 (1.2e-14***) -0.69 (0.065) -3.8 (2.2e-22***) -3 (2e-09***) -0.13 (0.17) 0.25 (0.0048**) 0.053 (0.62) 0.25 (0.067) -3.4 (2.9e-49***) 3.7 (1.7e-39***) -1 (1.7e-07***) 0.34 (0.12) 1.3 (2.4e-16***) 0.98 (1.9e-05***) -3.5 (5.4e-20***) 4.5 (6.5e-39***) 0.11 (0.76)
LEN^2 -0.6 (6.2e-19***) -0.083 (2.8e-05***) 0.034 (0.39) -0.11 (2.1e-07***) -0.19 (3.7e-33***) 0.2 (9.5e-08***) 0.41 (2.2e-28***) 0.14 (0.0083**) 0.29 (1.2e-17***) -0.17 (1.4e-30***) -0.11 (4e-30***) -0.17 (7.2e-13***) -0.21 (1.9e-18***) -0.2 (1.9e-10***) -0.0078 (0.19) 0.016 (0.0045**) 0.0035 (0.6) 0.016 (0.064) -0.23 (4.2e-56***) 0.25 (4.2e-44***) -0.068 (4.6e-08***) 0.022 (0.1) 0.076 (5.3e-15***) 0.06 (2.8e-05***) -0.33 (9e-42***) 0.24 (7.6e-29***) 0.065 (0.0065**)
vowel . (4e-194***) . (1.1e-311***) . (0***) . (0***) . (0***) . (1.4e-62***) . (2.3e-63***) . (5.8e-147***) . (0***) . (0***) . (8e-73***) . (0***) . (0***) . (0***) . (0***) . (8e-75***) . (0***) . (6.3e-260***) . (0***) . (1.7e-101***) . (0***) . (9.3e-55***) . (0***) . (0***) . (0***) . (0***) . (0***)
replication 5.2e-07 (1) -0.00015 (0.57) -0.00052 (0.34) 0.00027 (0.34) 0.00014 (0.51) -0.00024 (0.64) -0.00018 (0.72) -0.00029 (0.68) 3.1e-06 (0.99) -0.00023 (0.26) 3.3e-05 (0.81) 9.6e-05 (0.76) -8.6e-05 (0.8) 3.2e-05 (0.94) 4.7e-05 (0.56) 0.00011 (0.14) 3.1e-05 (0.73) -5.9e-05 (0.61) 4.7e-05 (0.81) 2.3e-05 (0.92) 0.0001 (0.54) -5e-06 (0.98) -0.00014 (0.29) -0.0002 (0.31) 0.00014 (0.68) -2.8e-05 (0.92) -4.3e-05 (0.9)
generation -0.0032 (4e-29***) 0.00075 (2.4e-19***) -0.0002 (0.23) -8.4e-05 (0.34) -4.9e-06 (0.94) -0.00045 (0.0045**) 0.00048 (0.0018**) 0.0007 (0.0011**) -1.1e-05 (0.94) -0.00045 (1.2e-12***) -2e-05 (0.63) 0.00019 (0.055) -0.00054 (9.5e-08***) -0.0003 (0.022*) -0.00024 (6.2e-22***) -0.00028 (5.6e-33***) -0.00013 (2.1e-06***) -0.0003 (1e-16***) 8.1e-05 (0.17) -0.00049 (1.8e-11***) -0.00028 (8.6e-08***) -0.00058 (6.6e-24***) -0.00033 (1.8e-16***) -0.00044 (4.6e-13***) -0.00013 (0.2) 8.5e-06 (0.92) -0.00045 (6.5e-06***)
LEN:vowel . (4.6e-28***) . (1.8e-53***) . (2e-42***) . (0***) . (2e-225***) . (2.4e-18***) . (1.4e-68***) . (3.5e-38***) . (2.2e-28***) . (5e-139***) . (2.1e-31***) . (5.8e-135***) . (1.3e-80***) . (4.2e-140***) . (1.1e-110***) . (3.2e-107***) . (0***) . (0***) . (4.1e-42***) . (2.9e-126***) . (1.1e-53***) . (2e-34***) . (7.6e-89***) . (5.6e-302***) . (4.8e-135***) . (1.4e-125***) . (4.9e-136***)
LEN^2:vowel . (2.1e-11***) . (0.00012***) . (0.0076**) . (4.1e-228***) . (5e-81***) . (4.9e-21***) . (3.6e-11***) . (1.3e-10***) . (5.2e-21***) . (4.4e-07***) . (2.5e-19***) . (9.1e-22***) . (1.9e-42***) . (2.9e-96***) . (8.8e-135***) . (4.3e-11***) . (2.2e-246***) . (2e-217***) . (5.4e-54***) . (1.2e-86***) . (1.5e-58***) . (3.1e-30***) . (0***) . (0***) . (1.9e-51***) . (2.1e-83***) . (2.4e-139***)
adjusted R2 34.6% 47.6% 49.2% 88.3% 78.1% 17.8% 40.7% 25.2% 55.4% 60.5% 87.0% 93.3% 87.6% 74.7% 99.5% 31.3% 99.8% 69.1% 72.9% 65.1% 55.8% 21.0% 73.7% 79.9% 94.5% 93.2% 90.7%
Regression of articulators on LEN, vowel and generation for mobile hyoid (with 95%CI).

Regression of articulators on LEN, vowel and generation for mobile hyoid (with 95%CI).

Regression of articulators on LEN, vowel and generation for mobile hyoid (with 95%CI).

Regression of articulators on LEN, vowel and generation for mobile hyoid (with 95%CI).

Regression of formants on LEN, vowel and generation for mobile hyoid (with 95%CI).

Regression of formants on LEN, vowel and generation for mobile hyoid (with 95%CI).

Regression of PCs on LEN, vowel and generation for mobile hyoid (with 95%CI).

Regression of PCs on LEN, vowel and generation for mobile hyoid (with 95%CI).

Articulators vs VTRatio (raw data).

Articulators vs VTRatio (raw data).